This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.

Group Theory
Symmetry
Permutation Groups
Representation
Sylow Theorems
Groups of Geometric Objects
Wallpaper Symmetry Groups
Set Theory
Combinatorics
Number Theory
Algebraic Structures
Lagrange’s Theorem
Normal Subgroups
Factor Groups
Homomorphisms

• Introduction to Group Theory

• Groups and Subgroups

• Cyclic Groups

• Permutation Groups

• Cosets and Lagrange’s Theorem

• Normal Subgroups and Quotient Groups

• Group Homomorphisms

• The Isomorphism Theorems

• Group Actions

• Sylow Theorems

• Applications of Group Theory

• Advanced Topics

• Department of Mathematics, Yazd University, Yazd, Iran

  Bijan Davvaz

Book Title
A First Course in Group Theory

Authors
Bijan Davvaz

DOI
https://doi.org/10.1007/978-981-16-6365-9

eBook Packages
Mathematics and Statistics, Mathematics and Statistics (R0)

Copyright Information
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

Hardcover ISBN
978-981-16-6364-2
Published: 11 November 2021

Softcover ISBN
978-981-16-6367-3
Published: 12 November 2022

eBook ISBN
978-981-16-6365-9
Published: 10 November 2021

Edition Number
1

Number of Pages
XV, 291

Number of Illustrations
4 b/w illustrations, 79 illustrations in colour

Topics
Group Theory and Generalizations, Number Theory, Linear Algebra