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