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010   $a1-4612-4176-6
024 7 $a10.1007/978-1-4612-4176-8
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035   $a(PQKBTitleCode)TC0001297280
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035   $a(PQKB)10222874
035   $a(DE-He213)978-1-4612-4176-8
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100   $a20121227d1995      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 13$aAn Introduction to the Theory of Groups /$fby Joseph J. Rotman
205   $a4th ed. 1995.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995.
215   $a1 online resource (XV, 517 p.) 
225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v148
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a0-387-94285-8 
311 08$a1-4612-8686-7 
320   $aIncludes bibliographical references and index.
327   $a1 Groups and Homomorphisms -- Permutations -- Cycles -- Factorization into Disjoint Cycles -- Even and Odd Permutations -- Semigroups -- Groups -- Homomorphisms -- 2 The Isomorphism Theorems -- Subgroups -- Lagrange?s Theorem -- Cyclic Groups -- Normal Subgroups -- Quotient Groups -- The Isomorphism Theorems -- Correspondence Theorem -- Direct Products -- 3 Symmetric Groups and G-Sets -- Conjugates -- Symmetric Groups -- The Simplicity of An -- Some Representation Theorems -- G-Sets -- Counting Orbits -- Some Geometry -- 4 The Sylow Theorems -- p-Groups -- The Sylow Theorems -- Groups of Small Order -- 5 Normal Series -- Some Galois Theory -- The Jordan-Hölder Theorem -- Solvable Groups -- Two Theorems of P. Hall -- Central Series and Nilpotent Groups -- p-Groups -- 6 Finite Direct Products -- The Basis Theorem -- The Fundamental Theorem of Finite Abelian Groups -- Canonical Forms; Existence -- Canonical Forms; Uniqueness -- The Krull?Schmidt Theorem -- Operator Groups -- 7 Extensions and Cohomology -- The Extension Problem -- Automorphism Groups -- Semidirect Products -- Wreath Products -- Factor Sets -- Theorems of Schur-Zassenhaus and Gaschütz -- Transfer and Burnside?s Theorem -- Projective Representations and the Schur Multiplier -- Derivations -- 8 Some Simple Linear Groups -- Finite Fields -- The General Linear Group -- PSL(2, K) -- PSL(m, K) -- Classical Groups -- 9 Permutations and the Mathieu Groups -- Multiple Transitivity -- Primitive G-Sets -- Simplicity Criteria -- Affine Geometry -- Projective Geometry -- Sharply 3-Transitivc Groups -- Mathieu Groups -- Steiner Systems -- 10 Abelian Groups -- Basics -- Free Abelian Groups -- Finitely Generated Abelian Groups -- Divisible and Reduced Groups -- Torsion Groups -- Subgroups of ? -- Character Groups -- 11 Free Groups and Free Products -- Generators and Relations -- SemigroupInterlude -- Coset Enumeration -- Presentations and the Schur Multiplier -- Fundamental Groups of Complexes -- Tietze?s Theorem -- Covering Complexes -- The Nielscn-Schreier Theorem -- Free Products -- The Kurosh Theorem -- The van Kampen Theorem -- Amalgams -- HNN Extensions -- 12 The Word Problem -- Turing Machines -- The Markov?Post Theorem -- The Novikov?Boone?Britton Theorem: Sufficiency of Boone?s Lemma -- Cancellation Diagrams -- The Novikov?Boone?Britton Theorem: Necessity of Boone?s Lemma -- The Higman Imbedding Theorem -- Some Applications -- Epilogue -- 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 -- Notation.
410  0$aGraduate Texts in Mathematics,$x2197-5612 ;$v148
606   $aGroup theory
606   $aGroup Theory and Generalizations
615  0$aGroup theory.
615 14$aGroup Theory and Generalizations.
676   $a512.2
700   $aRotman$b Joseph J$4aut$4http://id.loc.gov/vocabulary/relators/aut$058666
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910971121203321
996   $aIntroduction to the theory of groups$9376006
997   $aUNINA