Algebra: Set Theory, Natural Numbers and Graph Theory

Author(s): V. A. Hiremath

ISBN: 978-81-8487-724-3
E-ISBN: Publication Year: 2022
Pages: 352
Binding: Paper Back Dimension: 160mm x 240mm Weight: 500

Textbook

About the book

A self-contained text which begins with basic set theory and then onto advanced set theory. As the knowledge of natural numbers is very essential in the study of group theory, a separate chapter is devoted to the study of natural numbers. The rest of this volume is devoted to the study of natural numbers. The rest of this volume is devoted to group theory. Starting with the definition of a group, all basic results in group theory are proved. As permutation groups play an important role in group theory, a detailed study of permutation groups is taken up. Then Sylow theory is developed and a complete classification of groups of small orders is given. We conclude with the study of solvable groups.

Key Features

• An exhaustive list of exercises given at the end of each chapter helping readers to understand the concepts.
• Appendix covering important results – Frobenius theorem, complete groups and Phillip Hall’s theorems on solvable groups.

Table of Contents

Preface / Notations and Symbols / Mathematical Logic and Set Theory / Natural Numbers / Advanced Set Theory / Basic Group Theory / Permutation Groups / Sylow Theory / Solvable Groups and Jordan-Hölder Theorem / Appendix / Index.