96 Pages
by
CRC Press
90 Pages
by
CRC Press
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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.
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
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
