04467nam 22005175 450 991048021450332120200629220209.01-4612-4176-610.1007/978-1-4612-4176-8(CKB)3400000000090734(SSID)ssj0001297280(PQKBManifestationID)11724810(PQKBTitleCode)TC0001297280(PQKBWorkID)11363388(PQKB)10222874(DE-He213)978-1-4612-4176-8(MiAaPQ)EBC3075618(PPN)238036936(EXLCZ)99340000000009073420121227d1995 u| 0engurnn|008mamaatxtccrAn Introduction to the Theory of Groups[electronic resource] /by Joseph J. Rotman4th ed. 1995.New York, NY :Springer New York :Imprint: Springer,1995.1 online resource (XV, 517 p.) Graduate Texts in Mathematics,0072-5285 ;148Bibliographic Level Mode of Issuance: Monograph0-387-94285-8 1-4612-8686-7 Includes bibliographical references and index.1 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 -- Semigroup Interlude -- 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.Graduate Texts in Mathematics,0072-5285 ;148Group theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Group theory.Group Theory and Generalizations.512.2Rotman Joseph Jauthttp://id.loc.gov/vocabulary/relators/aut58666BOOK9910480214503321Introduction to the theory of groups376006UNINA