3-transpositions in infinite groups
Let G be a group. A subset D will be called a set of 3-transpositions if | x | = 2 for x e D and | xy | = 3 whenever x, yeD do not commute. We will call the set D closed if xDx −1 = D for each xeD . For each xeD , let For each subset X of D , we denote by [ X ] the graph with vertex set X where two elements x, yeX are joined by an edge whenever they commute. We denote by ( X ) the complement graph; thus two elements x, yeX are joined by an edge of ( X ) whenever they do not commute.

title: On a theorem of Goldschmidt

title: The nonexistence of 8-transitive graphs
abstract: We prove that the inequalitys≦7 holds for finites-transitive graphs assuming that the list of known 2-transitive permutation groups is complete.

title: A characterization of the group Co 3 as a transitive extension of HS

title: On Distance-Transitive Graphs
abstract: On suppose que Γ est un graphe non oriente connexe de genre fini g et G est un sous-groupe de aut(Γ) tel que pour chaque sommet x, G(x) est fini et agit transitivement sur l'ensemble des s-chemins (x 0 ,…,x s ) avec x 0 =x. Soit M un entier positif avec M≡3 (mod 8) et soit m=(M+9)/4 et n=max(2m+4,14). Si s≥2(m−1) et s≥(g−M)/2 alors Gm(x 0 ,…,x n )=1 pour chaque n-chemin (x 0 ,…,x n )

title: Graphs which are locally Grassmann

title: SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems
abstract: In spline approximation and in the numerical solution of (systems of) ordinary differential equations, one is eventually faced with linear systems of a rather characteristic, almost block diagonal, form which reflects the underlying geometry of the problems. While these systems could be treated as banded systems, it is more efficient, both in the generation of the systems and in their numerical solution, to work explicitly with their block structure. The report describes a package of FORTRAN routines for the solution of an almost block diagonal system by Gauss elimination with scaled row pivoting. Two examples are given. The first involves the solution of an m-th order ordinary differential equation by collocation. The second example offers a package of routines for the solution of a system of first order ODEs by collection at Lobatto points which is then used on a somewhat tricky reentry problem.

title: A Geometric Characterization of Certain Groups of Lie Type
abstract: Let r be an undirected graph with vertex set V(r) and edge set E(r) and let G be a subgroup of Aut (r). For each {x, y} E E(r), we denote by G{x, y} the stabilizer of {x, y} in G (which mayor may not contain elements exchanging the vertices x and y). For each x E V(r) we denote by r(x) the set of vertices adjacent to x, by G(x) the stabilizer of x in G and, for each i E N, by Gi(x) the subgroup {a E Gla E G(u) for all u E V(r) with a(x, u) "'" i} where a(x, u) denotes the distance from x to u. An s-path (for sEN) is an (s + I)-tuple (xo, Xl. .•• , xs ) of vertices such that Xi E r(Xi-l) if 1"", i "'" s and Xi ¥Xi-Z if 2"", i "'" s. Let G(xo, ... , xs ) = G(xo) n··· n G(xs ) and Gi(xo, ... , xs ) = Gi(xo) n· .. n Gi(xs ) for each s-path (xo, ... , xs ) and each i E N. If H is any group acting on a set X, we denote by H X the permutation group on X induced by H. . In  we proved the following result.

title: Product Integration for the Generalized Abel Equation
abstract: The solution of the generalized Abel integral equation g(t) f {k(t, s)/(t s)a}f (s) ds, 0 < a < 1, where k(t, s) is continuous, by the product integration analogue of the trapezoidal method is examined. It is shown that this method has order two convergence for a E [al, 1) with al 0.2117. This interval contains the important case a = 2. Convergence of order two for a E (0, al) is discussed and illustrated numerically. The possibility of constructing higher order methods is illustrated with an example.

title: Permutation groups with projective unitary subconstituents
abstract: AssTRAcT. Let r be a finite directed graph with vertex set V(I) and edge set EQ7) and let G be a subgroup of aut(I) which we assume to act transitively on both V(r) and E(r). Suppose that for some prime power q, the stabilizer G(x) of a vertex x induces on both {yI(x,y) E E(r)) and {wl(w, x) E E)} a group lying between PSU(3, q2) and Pr1U(3, q2). It is shown that if G acts primitively on V(I), then for each edge (x, y), the subgroup of G(x) fixing every vertex in {wI(x, w) or (y, w) E E(r)) is trivial.

title: On the Approximation of Fixed Points of Nonlinear Compact Operators
abstract: Certain methods for the approximate solution of $x - Kx = 0$, where K is a compact operator, lead to a family of operator equations $x - K_n x = 0$, $n \geqq 1$, where $K_n $,$n \geqq 1$, are collectively compact and converge pointwise to K. In this paper a new and simplified proof of the existence and uniqueness of a solution of $x - K_n x = 0$ in a neighborhood of an isolated solution of $x - Kx = 0$ is given.