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An introduction to the theory of groups
Autor: Rotman Joseph J.
Rok: 1995
ISBN: 9780387942858
ISBN: 9783540942856
OKCZID: 110112773
Vydání: 4th ed.
Citace (dle ČSN ISO 690):
ROTMAN, Joseph J.. An introduction to the theory of groups. 4th ed. New York ;: Berlin :, Springer, 1995, 513 s. Graduate texts in mathematics, 148. ISBN 0-387-94285-8.
Anotace
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).