An Introduction to Groups : A Computer Illustrated Text book cover
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1st Edition

An Introduction to Groups
A Computer Illustrated Text

By

D Asche




ISBN 9780429332401
Published February 27, 2021 by CRC Press
90 Pages

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Book Description

An Introduction to Groups: A Computer Illustrated Text discusses all the concepts necessary for a thorough understanding of group theory. The book covers various theorems, including Lagrange and Sylow. It also details Cayley tables, Burnside's lemma, homomorphisms, and dicyclic groups. The book is ideal for advanced mathematics students and beginning undergraduates.

Table of Contents

PERMUTATIONS
Notation
Products
Identity and Inverses
Order and Cycle Structure
Even and Odd Permutations

GROUPS
Basic Concepts and Notation
Subgroups and Cayley Tables
Cyclic Groups
Subgroups and Generators of Cyclic Groups
Cosets and Lagrange's Theorem

GROUP ACTIONS
Definition and Action Tables
Orbits and Stabilizers
Burnside's Lemma
Further Applications

CONJUGACY
Introduction
Conjugacy Classes
Normal Subgroups
The Sylow Theorems

HOMOMORPHISMS AND QUOTIENT GROUPS
Basic Concepts
Properties
The Kernel
Quotient Groups
An Isomorphism Theorem

CONSTRUCTING GROUPS
Direct Products
Dihedral Groups
Dicyclic Groups
More Constructions

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