Group theory : an expedition with sagemath

Includes bibliographical references and index.

Preface / About the Authors / List of Figures / Preliminaries / Introduction to Groups / Subgroups / Group Homomorphisms / Direct Product and Finite Abelian Groups / Group Actions / Sylow Theory / Introduction to SageMath / Group Theory and SageMath / Hints and Solutions / Bibliography / Index.

Group Theory: An Expedition with SageMath provides a rigorous introduction to the basics aspect group theory. In addition to the conventional group theory, the book introduces SageMath, a free open source computer algebra system based on Python programming language. The book is in parts. The first part is about an introduction to basic group theory, can be used as a standard textbook. The book contains many illustrative examples and exercises to help the reader to critically analyse appreciate various concepts in group theory. The second part is an attempt to demonstrate SageMath can be used as an effective tool to understand computational aspects of group theory.

Covers basic group theory, starting with the definition of groups, subgroups, generators and homomorphisms • Includes other topics like automorphism groups, fundamental theorem of finite abelian groups, group action with applications and classification of groups of small orders. • Each chapter includes large number of illustrative examples and exercises • Demonstrates SageMath as an effective tool to understand finite group theory • Numerous illustrative examples using SageMath are included to make the subject more interesting.