partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

a brief history of the classification of the finite simple groups first published in bulletin of the american mathematical society in volume 38 issue 3 published by the american mathematical society

modelling spatially correlated data via mixtures a bayesian approach the paper develops mixture models for spatially indexed data we confine attention to the case of finite typically irregular patterns of points or regions with prescribed spatial relationships and to problems where it is only the weights in the mixture that vary from one location to another our specific focus is on poisson distributed data and applications in disease mapping we work in a bayesian framework with the poisson parameters drawn from gamma priors and an unknown number of components we propose two alternative models for spatially dependent weights based on transformations of autoregressive gaussian processes in one the logistic normal model the mixture component labels are exchangeable in the other the grouped continuous model they are ordered reversible jump markov chain monte carlo algorithms for posterior inference are developed finally the performances of both of these formulations are examined on synthetic data and real data on mortality from a rare disease

the restricted simple lie algebras are of classical or cartan type abstract the classification of the finite dimensional restricted simple lie algebras over an algebraically closed field f of prime characteristic p 7 is announced such an algebra is either of classical type an analogue over f of a finite dimensional simple lie algebra over the complex numbers or of cartan type an analogue over f of one of the infinite lie algebras of cartan over the complex numbers

an equivariant analogue of glauberman s zj theorem we will prove an analogue of glauberman s zj theorem 4 and 6 theorem 8 2 1 p 279 that can be used to study finite groups that admit a coprime group of automorphisms this analogue is unusual in that no hypothesis of p stability is required used in conjunction with the bender method it may make it possible to prove very general results about finite groups that admit a coprime group of automorphisms the reader is referred to 7 and 8 for a fuller discussion of the bender method glauberman s zj theorem and p stability before stating the main result of this paper we introduce some notation if r and g are groups then we say that r acts coprimely on g if r acts as a group of automorphisms on g if r and g have coprime orders and if at least one of r or g is soluble suppose that r acts coprimely on g and that p is a prime define

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

dynamics of a family of chebyshev halley type methods in this paper the dynamics of the chebyshev halley family is studied on quadratic polynomials a singular set that we call cat set appears in the parameter space associated to the family this set has interesting similarities with the mandelbrot set the parameter space has allowed us to find different elements of the family which have bad convergence properties since periodic orbits and attractive strange fixed points appear in the dynamical plane of the corresponding method

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

nonsolvable signalizer functors on finite groups recently gorenstein and lyons obtained the first nonsolvable signalizer functor theorems 9 they pinpointed certain unbalancing problems this paper grew from an attempt to manage such problems theorem a is the result theorem b and corollary c give some measure of the practical scope of theorem a suppose p is a prime a is an elementary abelian p subgroup of a finite group g and 8 is an a signalizer functor on g the unbalancing difficulties referred to above occur only if there are certain nonidentity subgroups x of g such that c a is solvable using methods of glauberman s lemma 2 11 and theorem 4 51 we are able to reduce the problem either the unbalancing problems vanish or o c a is solvable the latter case is treated in 131 the rest of the work is treated here this work pivots on theorems 5 16 and 6 5 results which closely resemble 5 lemma 2 11 and theorem 4 5 1

rational rigidity and the sporadic groups the question of which finite groups can or do occur as the galois group of a galois extension of the rational numbers is one which has been studied since early in the twentieth century it is conjectured that all finite groups do occur as galois groups over the rationals this is known to be true for all solvable groups see jacobson 73 for brief historical notes in a breakthrough paper thompson 9 has defined the new concept of rigidity of a finite group he then proves that if a group g with trivial centre is rigid then an associated group g is a galois group over the rationals in this paper it is shown that 14 of the 26 sporadic simple groups are galois groups over the rationals the method used involves the complex character table and knowledge of maximal subgroups of the group in some cases where the maximal subgroups are not known the classification of finite simple groups is used section 1 contains the results section 2 describes the notation used and section 3 details the proof for each of the 14 groups separately

recursive computing and simulation free inference for general factorizable models summary we illustrate how the recursive algorithm of reeves pettitt 2004 for general factorizable models can be extended to allow exact sampling maximization of distributions and computation of marginal distributions all of the methods we describe apply to discrete valued markov random fields with nearest neighbour integrations defined on regular lattices in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices in this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as markov chain monte carlo in particular our work offers the basis for an automatic inference machine for such models

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

finite groups with dihedral sylow 2 subgroups it is mainly based on characterizations of p y q and a by brauer et al 4 and by suzuki 141 on the feit thompson odd order theorem 5 used throughout this paper without reference and on glauberman s zjtheorem 6 not available when gorenstein and walter proved their fundamental classification theorem our maximal subgroup approach is adopted from 11 it was glauberman s work 71 privately communicated which revived the author s interest in the subject via 3 it led to extensive simplifications of his original proof in the remainder of this section we list some elementary general facts in addition to standard notation we write f x for 0 y and 1 s for xex xs x j a group e is called quasisimple if 1 e e and e z e is simple

time series analysis of non gaussian observations based on state space models from both classical and bayesian perspectives the analysis of non gaussian time series by using state space models is considered from both classical and bayesian perspectives the treatment in both cases is based on simulation using importance sampling and antithetic variables markov chain monte carlo methods are not employed non gaussian disturbances for the state equation as well as for the observation equation are considered methods for estimating conditional and posterior means of functions of the state vector given the observations and the mean square errors of their estimates are developed these methods are extended to cover the estimation of conditional and posterior densities and distribution functions the choice of importance sampling densities and antithetic variables is discussed the techniques work well in practice and are computationally efficient their use is illustrated by applying them to a univariate discrete time series a series with outliers and a volatility series

on an application of symbolic computation and computer graphics to root finders the contemporary powerful mathematical software enables a new approach to handling and manipulating complex mathematical expressions and other mathematical objects particularly the use of symbolic computation leads to new contribution to constructing and analyzing numerical algorithms for solving very difficult problems in applied mathematics and other scientific disciplines in this paper we are concerned with the problem of determining multiple zeros when the multiplicity is not known in advance a task that is seldom considered in literature by the use of computer algebra system mathematica we employ symbolic computation through several programs to construct and investigate algorithms which both determine a sought zero and its multiplicity applying a recurrent formula for generating iterative methods of higher order for solving nonlinear equations we construct iterative methods that serve i for approximating a multiple zero of a given function f when the order of multiplicity is unknown and simultaneously ii for finding exact order of multiplicity in particular we state useful cubically convergent iterative sequences that find the exact multiplicity in a few iteration steps such approach combined with a rapidly convergent method for multiple zeros provides the construction of efficient composite algorithms for finding multiple zeros of very high accuracy the properties of the proposed algorithms are illustrated by several numerical examples and basins of attraction

updating schemes correlation structure blocking and parameterization for the gibbs sampler in this paper many convergence issues concerning the implementation of the gibbs sampler are investigated exact computable rates of convergence for gaussian target distributions are obtained different random and non random updating strategies and blocking combinations are compared using the rates the effect of dimensionality and correlation structure on the convergence rates are studied some examples are considered to demonstrate the results for a gaussian image analysis problem several updating strategies are described and compared for problems in bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice

on some simultaneous methods based on weierstrass correction abstract the purpose of the paper is to present some procedures for the construction of simultaneous methods for finding all zeros of a polynomial f using weierstrass corrections w i z f z k i z z k in this manner some well known methods as well as new methods are obtained the proposed iterative algorithms are realized in ordinary complex arithmetic and circular interval arithmetic the convergence analysis of the presented methods and numerical examples are given

detection of gauss markov random fields with nearest neighbor dependency the problem of hypothesis testing against independence for a gauss markov random field gmrf is analyzed assuming an acyclic dependency graph an expression for the log likelihood ratio of detection is derived assuming random placement of nodes over a large region according to the poisson or uniform distribution and nearest neighbor dependency graph the error exponent of the neyman pearson detector is derived using large deviations theory the error exponent is expressed as a dependency graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals the exponent is analyzed for different values of the variance ratio and correlation it is found that a more correlated gmrf has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio

deviance information criterion for latent variable models and misspecified models abstract deviance information criterion dic has been widely used for bayesian model comparison especially after markov chain monte carlo mcmc is used to estimate candidate models this paper first studies the problem of using dic to compare latent variable models when dic is calculated from the conditional likelihood in particular it is shown that the conditional likelihood approach undermines theoretical underpinnings of dic a new version of dic namely dic l is proposed to compare latent variable models the large sample properties of dic l are studied a frequentist justification of dic l is provided like aic dic l provides an asymptotically unbiased estimator to the expected kullback leibler kl divergence between the dgp and a predictive distribution some popular algorithms such as the em kalman and particle filtering algorithms are introduced to compute dic l for latent variable models moreover this paper studies the problem of using dic to compare misspecified models a new version of dic namely dic m is proposed and it can be regarded as a bayesian version of tic a frequentist justification of dic m is provided under misspecification dic l and dic m are illustrated using asset pricing models and stochastic volatility models

the hessian method highly efficient simulation smoothing in a nutshell abstract i introduce the hessian highly efficient simulation smoothing in a nutshell method for numerically efficient simulation smoothing in state space models with univariate states given a vector of parameters the vector of states 1 n is gaussian and the observed vector y y 1 y n need not be i describe a procedure to construct a close approximation q y to the target density p y it requires code to compute five derivatives of log p y t t with respect to t t 1 n and is not otherwise model specific since q y is proper fully normalised and simulable it can be used as an importance density for importance sampling is or as a proposal density for markov chain monte carlo mcmc hessian is an acronym but it also refers to the sparse hessian matrix of log p y with respect to the hessian method is based on sparse matrix operations rather than the kalman filter i construct q y and a related approximation q y of p y for two stochastic volatility models two stochastic count models and a stochastic duration model i illustrate their use for numerical approximation of likelihood function values and marginal likelihoods using is and for posterior inference using is and mcmc compared with other simulation smoothing methods the hessian method is highly numerically efficient in an is application featuring a student s t stochastic volatility model and n 8851 daily log returns the efficiency of is for numerical approximation of the elements of the posterior mean e y is between 80 and 100

a construction of attracting periodic orbits for some classical third order iterative methods we use a family of root finding iterative methods for finding roots of nonlinear equations we present a procedure for constructing polynomials so that superattracting periodic orbits of any prescribed period occur when these methods are applied this family includes chebyshev s method halley s method the super halley method and the c methods as particular cases

on newton type methods for multiple roots with cubic convergence we introduce two families of newton type methods for multiple roots with cubic convergence a further newton type method for multiple roots with cubic convergence is presented that is related to quadrature we also provide numerical tests that show that these new methods are competitive to other known methods for multiple roots

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

resolution of singularities and modular galois theory i shall sketch a brief history of the desingularization problem from riemann thru zariski to hironaka including the part i played in it and the work on galois theory which this led me to and how that caused me to search out many group theory gurus i shall also formulate several conjectures and suggest numerous thesis problems

standard 3 components of type sl 4 2 abstract aschbacher s recent work on finite simple groups g with e g 3 has led to the following problem find all finite simple groups g which contain an element b of order 3 such that c b contains a normal quasi simple subgroup l with l z l sl 4 2 and such that certain further conditions hold this paper solves that problem

rcg r signalizers in finite groups abstract let r be a prime and suppose the r group r acts as a group of automorphisms on the r group g we study the rc g r invariant subgroups of g and how they influence the structure of g an application to the study of the automorphism group of a simple group is presented

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

asymptotic error constants of cubically convergent zero finding methods the laguerre family of iteration functions for finding multiple zeros is considered this family is algebraically equivalent to the multiple zero counterpart of hansen patrick family the asymptotic error constant for the laguerre family is given the magnitude of asymptotic error constants for cubically convergent iteration functions for finding multiple real zeros of real functions are compared numerical examples are given

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

a new proof of the solvable signalizer functor theorem abstract a new proof of glauberman s solvable signalizer functor theorem is presented the solvable signalizer functor theorem is one of the background results needed for the new proof of the classification of the finite simple groups in the gorenstein lyons solomon book series

a one parameter family of locally quartically convergent zero finding methods a one parameter family of iteration functions for finding simple and multiple zeros of analytic functions is derived the family includes as a special case traub s quartic square root method and as limiting cases the kiss method of order 4 the halley and the newton methods all the methods of the family are locally quartically convergent for a simple or multiple zero with known multiplicity the asymptotic error constants for the methods of the family are given the decreasing ratio at infinity of iteration functions is discussed the optimum parameter of the family for polynomials is given

a hall higman shult type theorem for arbitrary finite groups we shall extend a fixed point theorem of shult to arbitrary finite groups this will have applications to the study of group automorphisms

on the convergence of high order gargantini farmer loizou type iterative methods for simultaneous approximation of polynomial zeros abstract in 1984 kyurkchiev et al constructed an infinite sequence of iterative methods for simultaneous approximation of polynomial zeros with known multiplicity the first member of this sequence of iterative methods is the famous root finding method derived independently by farmer and loizou 1977 and gargantini 1978 for every given positive integer n the nth method of this family has the order of convergence 2 n 1 in this paper we prove two new local convergence results for this family of iterative methods the first one improves the result of kyurkchiev et al 1984 we end the paper with a comparison of the computational efficiency the convergence behavior and the computational order convergence of different methods of the family

empirical supremum rejection sampling reference stat article 2002 003doi 10 1093 biomet 89 4 745view record in web of science record created on 2006 04 21 modified on 2017 05 12

fast sampling of gaussian markov random fields this paper demonstrates how gaussian markov random fields conditional autoregressions can be sampled quickly by using numerical techniques for sparse matrices the algorithm is general and efficient and expands easily to various forms for conditional simulation and evaluation of normalization constants we demonstrate its use by constructing efficient block updates in markov chain monte carlo algorithms for disease mapping

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

chebyshev halley methods for analytic functions two modifications of the family of chebyshev halley methods are given the first is to improve the rate of convergence to a multiple zero of an analytic function the second is to find simultaneously all distinct zeros of a polynomial

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

bayesian analysis of agricultural field experiments the paper describes bayesian analysis for agricultural field experiments a topic that has received very little previous attention despite a vast frequentist literature adoption of the bayesian paradigm simplifies the interpretation of the results especially in ranking and selection also complex formulations can be analysed with comparative ease by using markov chain monte carlo methods a key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns this is discussed in detail problems caused by outliers and by jumps in fertility are tackled via hierarchical f formulations that may find use in other contexts the paper includes three analyses of variety trials for yield and one example involving binary data none is entirely straightforward some numerical comparisons with frequentist analyses are made

bayesian prediction of spatial count data using generalized linear mixed models summary spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a bayesian approach and markov chain monte carlo informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling furthermore we demonstrate that so called langevin hastings updates are useful for efficient simulation of the posterior distributions and we discuss computational issues concerning prediction

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

a new fourth order family of simultaneous methods for finding polynomial zeros using a suitable fixed point relation with a complex parameter a new one parameter family of simultaneous methods of the fourth order for finding complex zeros of a polynomial is derived in ordinary complex arithmetic convergence analysis of the presented family is performed under computationally verifiable initial conditions which depend only on polynomial coefficients and initial approximations further improvements of the proposed family of methods are discussed and a modification for finding multiple zeros is presented some numerical results for various values of the parameter are given

automatic bayesian curve fitting summary a method of estimating a variety of curves by a sequence of piecewise polynomials is proposed motivated by a bayesian model and an appropriate summary of the resulting posterior distribution a joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials throughout we use reversible jump markov chain monte carlo methods to compute the posteriors the methodology has been successful in giving good estimates for smooth functions i e continuous and differentiable as well as functions which are not differentiable and perhaps not even continuous at a finite number of points the methodology is extended to deal with generalized additive models

bayesian semiparametric intensity estimation for inhomogeneous spatial point processes summary in this work we propose a fully bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process the basic idea is to first convert intensity estimation into a poisson regression setting via binning data points on a regular grid and then model the log intensity semiparametrically using an adaptive version of gaussian markov random fields to smooth the corresponding counts the inference is carried by an efficient markov chain monte carlo simulation algorithm compared to existing methods for intensity estimation for example parametric modeling and kernel smoothing the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates but also uses information from the data to adaptively determine the amount of smoothing at the local level the effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

characters of finite groups with dihedral sylow 2 subgroups in this article we give alternate proofs of some intermediate results in the gorenstein walter classification 6 of groups with dihedral sylow 2subgroups these intermediate results will be applied in an alternate proof 1 of the entire classification by the first author our proofs rely only on elementary character theory and do not use block theory but they are motivated by the related work of brauer 2 and of gorenstein and walter 6 propositions l 41 which was obtained by block theory now we describe the situation which will be assumed in the following sections and in the three theorems stated below for elementary properties of groups with dihedral sylow 2 subgroups the reader is referred to s section 7 71

automorphisms of k groups i abstract this is the first in a sequence of papers that will develop the theory of automorphisms of nonsolvable finite groups the sequence will culminate in a new proof of mcbride s nonsolvable signalizer functor theorem which is one of the fundamental results required for the proof of the classification of the finite simple groups