An Introduction to the Theory of Groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1995
|
| Edition: | Fourth Edition |
| Series: | Graduate Texts in Mathematics
148 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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) |
| Physical Description: | 1 Online-Ressource (XV, 517 p) |
| ISBN: | 9781461241768 9781461286868 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4176-8 |
Staff View
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Record in the Search Index
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| edition | Fourth Edition |
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| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut An Introduction to the Theory of Groups by Joseph J. Rotman Fourth Edition New York, NY Springer New York 1995 1 Online-Ressource (XV, 517 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 148 0072-5285 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) Mathematics Group theory Group Theory and Generalizations Mathematik Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Gruppentheorie (DE-588)4072157-7 s 2\p DE-604 Gruppe Mathematik (DE-588)4022379-6 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-4176-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rotman, Joseph J. 1934- An Introduction to the Theory of Groups Mathematics Group theory Group Theory and Generalizations Mathematik Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4022379-6 (DE-588)4072157-7 (DE-588)4151278-9 |
| title | An Introduction to the Theory of Groups |
| title_auth | An Introduction to the Theory of Groups |
| title_exact_search | An Introduction to the Theory of Groups |
| title_full | An Introduction to the Theory of Groups by Joseph J. Rotman |
| title_fullStr | An Introduction to the Theory of Groups by Joseph J. Rotman |
| title_full_unstemmed | An Introduction to the Theory of Groups by Joseph J. Rotman |
| title_short | An Introduction to the Theory of Groups |
| title_sort | an introduction to the theory of groups |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik Gruppe Mathematik Gruppentheorie Einführung |
| url | https://doi.org/10.1007/978-1-4612-4176-8 |
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