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AuthorRotman, Joseph J. author
TitleAn Introduction to the Theory of Groups [electronic resource] / by Joseph J. Rotman
ImprintNew York, NY : Springer New York : Imprint: Springer, 1995
Edition Fourth Edition
Connect tohttp://dx.doi.org/10.1007/978-1-4612-4176-8
Descript XV, 517 p. online resource

CONTENT

1 Groups and Homomorphisms -- Permutations -- Cycles -- Factorization into Disjoint Cycles -- Even and Odd Permutations -- Semigroups -- Groups -- Homomorphisms -- 2 The Isomorphism Theorems -- Subgroups -- Lagrangeโ{128}{153}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-Hรถlder 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 Krullโ{128}{148}Schmidt Theorem -- Operator Groups -- 7 Extensions and Cohomology -- The Extension Problem -- Automorphism Groups -- Semidirect Products -- Wreath Products -- Factor Sets -- Theorems of Schur-Zassenhaus and Gaschรผtz -- Transfer and Burnsideโ{128}{153}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 -- Tietzeโ{128}{153}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 Markovโ{128}{148}Post Theorem -- The Novikovโ{128}{148}Booneโ{128}{148}Britton Theorem: Sufficiency of Booneโ{128}{153}s Lemma -- Cancellation Diagrams -- The Novikovโ{128}{148}Booneโ{128}{148}Britton Theorem: Necessity of Booneโ{128}{153}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 Zornโ{128}{153}s Lemma -- APPENDIX V Countability -- APPENDIX VI Commutative Rings -- Notation


Mathematics Group theory Mathematics Group Theory and Generalizations



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