An Introduction to the Theory of Groups / / by Joseph J. Rotman

• Autore: Rotman Joseph J
• Pubblicazione: New York, NY : , : Springer New York : , : Imprint : Springer, , 1995
• Edizione: 4th ed. 1995.
• Descrizione fisica: 1 online resource (XV, 517 p.)
• Disciplina: 512.2
• Soggetto topico: Group theory; Group Theory and Generalizations
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 -- 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.
• Titolo autorizzato: Introduction to the theory of groups
• ISBN: 1-4612-4176-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910971121203321
• Lo trovi qui: Univ. Federico II
• Serie: Graduate Texts in Mathematics, . 2197-5612 ; ; 148