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An Introduction to the Theo...
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)
Monografía
monografia Rebiun28152373 https://catalogo.rebiun.org/rebiun/record/Rebiun28152373 m o d cr |n||||||||| 170116s2014 xx o 000 0 eng d 852788209 1113635683 1159664268 1252630825 9781461241768 electronic bk.) 1461241766 electronic bk.) 9781461286868 1461286867 9780387942858 10.1007/978-1-4612-4176-8 doi AU@ 000051719849 NLGGC 401211673 NZ1 14981774 NZ1 15312455 YDX eng YDX OCLCQ AU@ GW5XE OCLCF COO UAB U3W TKN LEAUB UKBTH UKAHL N$T OCLCO PBG bicssc MAT002010 bisacsh 512.2 23 An Introduction to the Theory of Groups Springer Verlag 2014 Springer Verlag 1 online resource 1 online resource Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF Graduate Texts in Mathematics 0072-5285 148 Groups and Homomorphisms -- The Isomorphism Theorems -- Symmetric Groups and G-Sets -- The Sylow Theorems -- Normal Series -- Finite Direct Products -- Extensions and Cohomology -- Some Simple Linear Groups -- Permutations and Mathieu Groups -- Abelian Groups -- Free Groups and Free Products -- The Word Problem -- Appendices: Some Major Algebraic Systems -- Equivalence Relations and Equivalence Classes -- Functions -- Zorn's Lemma -- Countability -- Commutative Rings -- Bibliography -- Notation -- Index 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) English Mathematics Group theory Group theory. Mathematics. Electronic books Rotman, Joseph Original 9781461286868 1461286867 (OCoLC)886494953 Graduate texts in mathematics 148