The theory of groups : an introduction / [by] Joseph J. Rotman.
Series The Allyn and Bacon series in advanced mathematicsEditor: Boston : Allyn and Bacon, 1965Descripción: xiii, 305 p. ; 24 cmTema(s): Group theoryOtra clasificación: 20-01CONTENTS PREFACE vii 1. GROUPS AND HOMOMORPHISMS [2] 2. THE ISOMORPHISM THEOREMS Subgroups [15] Normal Subgroups and Quotient Groups [21] The Isomorphism Theorems [24] The Correspondence Theorem [27] 3. PERMUTATION GROUPS Permutations [31] Cycles [32] Conjugates [38] The Simplicity of An [42] Some Representation Theorems [46] Counting Orbits [49] 4. FINITE DIRECT PRODUCTS Direct Products [55] The Basis Theorem [58] The Fundamental Theorem of Finite Abelian Groups [62] Modules and Matrices [66] The Remak-Krull-Schmidt Theorem [76] 5. THE SYLOW THEOREMS p-Groups [85] The Sylow Theorems [87] Some Applications of the Sylow Theorems [91] 6. NORMAL AND SUBNORMAL SERIES Some Galois Theory [99] The Jordan-Holder Theorem [108] Solvable Groups [112] A Theorem of P. Hall [116] Central Series and Nilpotent Groups [119] 7. EXTENSIONS The Extension Problem [127] Automorphism Groups [129] Semidirect Products [133] Factor Sets [139] The Schur-Zassenhaus Lemma [144] 8. SOME SIMPLE GROUPS Finite Fields [149] The General Linear Group [155] PSL (2,K) [161] PSL (m,K) [165] 9. INFINITE ABELIAN GROUPS s The First Reduction: Torsion and Torsion-Free [175] The Second Reduction: Divisible and Reduced [180] Free Abelian Groups [187] Finitely Generated Abelian Groups [192] Torsion Groups [194] Torsion-Free Groups [200] 10. HOMOLOGICAL ALGEBRA [200] The Hom Functors [207] Definition of Ext [214] Pull-Backs and Push-Outs [215] The Ext Functors [225] 11. FREE GROUPS AND FREE PRODUCTS Generators and Relations [235] The Subgroup Theorem [242] Free Products [247] Free Products with Amalgamated Subgroups [250] 12. THE WORD PROBLEM Statement of the Problem; Turing Machines [257] Britton’s Lemma [265] The Novikov-Boone Theorem [271] APPENDICES I Some Major Algebraic Systems [283] II Equivalence Relations and Equivalence Classes [285] III Functions [287] IV Zorn’s Lemma [289] V Principal Ideal Domains [291] BIBLIOGRAPHY [295] SPECIAL NOTATIONS [296] INDEX [301]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 20 R848 (Browse shelf) | Available | A-2675 |
Bibliografía: p. 295.
CONTENTS --
PREFACE vii --
1. GROUPS AND HOMOMORPHISMS [2] --
2. THE ISOMORPHISM THEOREMS --
Subgroups [15] --
Normal Subgroups and Quotient Groups [21] --
The Isomorphism Theorems [24] --
The Correspondence Theorem [27] --
3. PERMUTATION GROUPS --
Permutations [31] --
Cycles [32] --
Conjugates [38] --
The Simplicity of An [42] --
Some Representation Theorems [46] --
Counting Orbits [49] --
4. FINITE DIRECT PRODUCTS --
Direct Products [55] --
The Basis Theorem [58] --
The Fundamental Theorem of Finite Abelian Groups [62] --
Modules and Matrices [66] --
The Remak-Krull-Schmidt Theorem [76] --
5. THE SYLOW THEOREMS --
p-Groups [85] --
The Sylow Theorems [87] --
Some Applications of the Sylow Theorems [91] --
6. NORMAL AND SUBNORMAL SERIES --
Some Galois Theory [99] --
The Jordan-Holder Theorem [108] --
Solvable Groups [112] --
A Theorem of P. Hall [116] --
Central Series and Nilpotent Groups [119] --
7. EXTENSIONS --
The Extension Problem [127] --
Automorphism Groups [129] --
Semidirect Products [133] --
Factor Sets [139] --
The Schur-Zassenhaus Lemma [144] --
8. SOME SIMPLE GROUPS --
Finite Fields [149] --
The General Linear Group [155] --
PSL (2,K) [161] --
PSL (m,K) [165] --
9. INFINITE ABELIAN GROUPS --
s The First Reduction: Torsion and Torsion-Free [175] --
The Second Reduction: Divisible and Reduced [180] --
Free Abelian Groups [187] --
Finitely Generated Abelian Groups [192] --
Torsion Groups [194] --
Torsion-Free Groups [200] --
10. HOMOLOGICAL ALGEBRA [200] --
The Hom Functors [207] --
Definition of Ext [214] --
Pull-Backs and Push-Outs [215] --
The Ext Functors [225] --
11. FREE GROUPS AND FREE PRODUCTS --
Generators and Relations [235] --
The Subgroup Theorem [242] --
Free Products [247] --
Free Products with Amalgamated Subgroups [250] --
12. THE WORD PROBLEM --
Statement of the Problem; Turing Machines [257] --
Britton’s Lemma [265] --
The Novikov-Boone Theorem [271] --
APPENDICES --
I Some Major Algebraic Systems [283] --
II Equivalence Relations and Equivalence Classes [285] --
III Functions [287] --
IV Zorn’s Lemma [289] --
V Principal Ideal Domains [291] --
BIBLIOGRAPHY [295] --
SPECIAL NOTATIONS [296] --
INDEX [301] --
MR, 34 #4338
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