Groups

With Holder's program used throughout for the classification of finite groups, this volume covers the key topics, including abelian, nilpotent and solvable groups, linear representations and cohomology. Group actions and the word problem are also considered.

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 given type are there, and how can they be described? Hölder's program for attacking this problem in the case of finite groups is a sort of leitmotiv 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 and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.

More than 400 exercises for almost all of which a solution is provided, help the reader check his/her comprehension of the text Some topics like representation theory, word problem or the meaning of some group-theoretic concepts in cohomology of groups are usually found in more specialized books The meaning of some group-theoretic concepts in Galois theory Includes supplementary material: sn.pub/extras

Contenu
Normal Subgroups, Conjugation and Isomorphism Theorems.- Group Actions and Permutation Groups.- Generators and Relations.- Nilpotent Groups and Solvable Groups.- Representations.- Extensions and Cohomology.- Solution to the exercises.