Introduction to the Theory of Groups
Edition: 4th 1995 (Revised)
List price: $79.99
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Description: Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions. The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem. The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to G-sets, a construction of the sporadic Mathieu groups).
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $79.99
Copyright year: 1995
Publication date: 8/13/1999
Size: 6.25" wide x 9.50" long x 0.75" tall
|Preface to the Fourth Edition|
|From Preface to the Third Edition|
|To the Reader|
|Groups and Homomorphisms|
|The Isomorphism Theorems|
|Symmetric Groups and G-Sets|
|The Sylow Theorems|
|Finite Direct Products|
|Extensions and Cohomology|
|Some Simple Linear Groups|
|Permutations and the Mathieu Groups|
|Free Groups and Free Products|
|The Word Problem|
|Appendix I: Some Major Algebraic Systems|
|Appendix II: Equivalence Relations and Equivalence Classes|
|Appendix III: Functions|
|Appendix IV: Zorn's Lemma|
|Appendix V: Countability|
|Appendix VI: Commutative Rings|