Algebra through Practice: A Collection of Problems in Algebra with Solutions. Groups

Byth T.S., Robertson E.F.0521212904

Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each volume is divided into sections that begin with some notes on notation and prerequisites. The majority of the material is aimed at the students of average ability but some sections contain more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other problems. Books later in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.

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Table of contents :
Groups……Page 1
Contents……Page 4
Preface……Page 5
Background reference material……Page 6
1. Subgroups……Page 8
2. Automorphisms and Sylow theory……Page 17
3. Series……Page 22
4. Presentations……Page 29
Solutions to Chapter 1……Page 36
Solutions to Chapter 2……Page 58
Solutions to Chapter 3……Page 69
Solutions to Chapter 4……Page 86
Test paper 1……Page 101
Test paper 2……Page 103
Test paper 3……Page 105
Test paper 4……Page 107
Back cover……Page 109