Well-organized and clearly written, this undergraduate-level text covers most of the standard basic theorems in group theory, providing proofs of the basic theorems of both finite and infinite groups and developing as much of their superstructure as space permits. Contents include: Isomorphism Theorems, Direct Sums, p-Groups and p-Subgroups, Free Groups and Free Products, Permutation Groups, Transformations and Subgroups, Abelian Groups, Supersolvable Groups, Extensions, Representations, and more.
The concluding chapters also cover a wide variety of further theorems, some not previously published in book form, including infinite symmetric and alternating groups, products of subgroups, the multiplicative group of a division ring, and FC groups.
Over 500 exercises in varying degrees of difficulty enable students to test their grasp of the material, which is largely self-contained (except for later chapters which presuppose some knowledge of linear algebra, polynomials, algebraic integers, and elementary number theory). Also included are a bibliography, index, and an index of notation.
Ideal as a text or for reference, this inexpensive paperbound edition of Group Theory offers mathematics students a lucid, highly useful introduction to an increasingly vital mathematical discipline. It will be welcomed by anyone in search of a cogent, thorough presentation that lends itself equally well to self-study or regular course work.