1st Edition

An Introduction to Groups A Computer Illustrated Text

By D Asche Copyright 1989

    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

    Biography

    D Asche (Author)