Groups : an introduction to ideas and methods of the theory of groups

Abstract

Groups are a means of classification, via the group action on a set,but also the object of a classification. How many groups of a giventype are there, and how can they be described? Hölder's program forattacking this problem in the case of finite groups is a sort ofleitmotiv throughout the text. Infinite groups are also considered,with particular attention to logical and decision problems. Abelian,nilpotent and solvable groups are studied both in the finite andinfinite case. Permutation groups and are treated in detail; theirrelationship with Galois theory is often taken into account. Thelast two chapters deal with the representation theory of finite groupand the cohomology theory of groups; the latter with special emphasison the extension problem. The sections are followed by exercises;hints to the solution are given, and for most of them a completesolution is provided.