num_pages: 166
description: With over 60 figures tables and diagrams this text is both an intuitive introduction to and a rigorous study of finite symmetric inverse semigroups. The model denoted $Cn$ consists of all charts (one-one partial transformations) of the set ${1\dotsn}$ under the usual composition of mappings. It has the symmetric groups $Sn$ as a subgroup and many classical features of $Sn$ are extended to $Cn$. It turns out that these semigroups enjoy many of the classical features of finite symmetric groups. For example cycle notation conjugacy commutativity parity of permutations alternating subgroups Klein 4-group Ruffini's result on cyclic groups Moore's presentations of the symmetric and alternating groups and the centralizer theory of symmetric groups are extended to more general counterparts in $Cn$. Lipscomb classifies normal subsemigroups and also illustrates and applies an Eilenberg-style wreath product. The basic $Cn$ theory is further extended to partial transformation semigroups and the Reconstruction Conjecture of graph theory is recast as a Rees' ideal-extension conjecture. This books presents much of the material on the theory of finite symmetric inverse semigroups unifying the classical finite symmetric group theory with its semigroup analogue. A comment section at the end of each chapter provides historical perspective. New proofs new theorems and the use of multiple figures tables and diagrams to present complex ideas make this book current and highly readable.
language: English
title: Symmetric Inverse Semigroups
publisher: American Mathematical Society