Groups : An Introduction to Ideas and Methods of the Theory of Groups

Antonio Machì

ISBN 10: 884702420X / ISBN 13: 9788847024205

Published by Springer, Springer, 2012

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9788847024205

Bibliographic Details

• Title: Groups : An Introduction to Ideas and Methods of the Theory of Groups
• Publisher: Springer, Springer
• Publication Date: 2012
• Language: English
• ISBN 10: 884702420X
• ISBN 13: 9788847024205
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 22D millimeters 235 millimeters width by 155 millimeters height by 22 millimeters depth
• Weight: 598 grams

About this title

Synopsis

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.