Fundamentals of group theory: an advanced approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
Birkhäuser
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 380 S. 24 cm |
| ISBN: | 9780817683009 |
Internformat
MARC
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| 003 | DE-604 | ||
| 005 | 20120601 | ||
| 007 | t | ||
| 008 | 120314s2012 |||| 00||| eng d | ||
| 020 | |a 9780817683009 |9 978-0-8176-8300-9 | ||
| 035 | |a (OCoLC)785850539 | ||
| 035 | |a (DE-599)BVBBV039957304 | ||
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| 041 | 0 | |a eng | |
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| 100 | 1 | |a Roman, Steven |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of group theory |b an advanced approach |c Steven Roman |
| 264 | 1 | |a Boston |b Birkhäuser |c 2012 | |
| 300 | |a XII, 380 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024815107 | ||
Datensatz im Suchindex
| _version_ | 1804148930801303552 |
|---|---|
| adam_text | Contents
Preface,
vii
1
Preliminaries«
1
Multisets,
1
Words.
1
Partially Ordered Sets,
2
Chain Conditions and Finiteness.
5
Lattices,
8
Equivalence Relations.
10
Cardinality.
12
Miscellanea.
15
2
Groups and Subgroups«
19
Operations on Sets.
19
Groups.
19
The Order of a Product,
26
Orders and Exponents,
28
Conjugation,
29
The Set Product,
31
Subgroups,
32
Finitely-Generated Groups,
35
The Lattice of Subgroups of a Group,
37
C osets
and Lagrange s Theorem,
41
Euleťs
Formula,
43
Cyclic Groups,
44
Hornomorphisms of Groups,
46
More Groups,
46
•An Historical Perspective: Galois-Style Groups.
56
Exercises,
58
3
Cosets, Index and Normal Subgroups,
61
Cosets and Index.
61
Quotient Groups and Normal Subgroups.
65
Internal Direct Products,
72
Chain Conditions and Subnormality.
76
ΙΛ
Contents
Subgroups of
Index 2, 78
Cauchy s Theorem,
79
The Center of a Group; Centralizers,
81
The Normalizer of a Subgroup,
82
Simple Groups,
84
Commutators of Elements,
84
Commutators of Subgroups,
93
* Multivariable
Commutators,
95
Exercises,
98
Homomorphisms, Chain Conditions and Subnormality,
105
Homomorphisms,
105
Kernels and the Natural Projection,
108
Groups of Small Order,
108
A Universal Property and the Isomorphism Theorems,
110
The Correspondence Theorem,
113
Group Extensions,
115
Inner Automorphisms,
119
Characteristic Subgroups,
120
Elementary
Abel i
an Groups,
121
Multiplication as a Permutation,
123
The Frattini Subgroup of a Group,
127
Subnormal Subgroups,
128
Chain Conditions,
136
Automorphisms of Cyclic Groups,
141
Exercises,
144
Direct and Semidirect Products,
149
Complements and Essentially Disjoint Products,
149
Product Decompositions,
151
Direct Sums and Direct Products,
152
Cancellation in Direct Sums,
157
The Classification of Finite Abelian Groups,
158
Properties of Direct Summands,
161
xY-Groups,
164
Behavior Under Direct Sum,
167
When All Subgroups Are Normal,
169
Semidirect Products,
171
The External Semidirect Product,
175
♦The Wreath Product,
180
Exercises,
185
Permutation Groups,
191
The Definition and Cycle Representation,
191
A Fundamental Formula Involving Conjugation,
193
Parity,
194
Generating Sets for Sn and An,
195
Contents xi
Subgroups of
Sn
and An,
197
The Alternating Group Is Simple,
197
Some Counting,
200
Exercises,
202
7
Group Actions; The Structure of p-Groups,
207
Group Actions,
207
Congruence Relations on
a G-S et,
211
Translation by
G,
212
Conjugation by
G on
the Conjugates of a Subgroup,
214
Conjugation by
G on a
Normal Subgroup,
214
The Structure of Finite p-Groups,
215
Exercises,
229
8
Sylow Theory,
235
Sylow Subgroups,
235
The Normalizer of a Sylow Subgroup,
235
The Sylow Theorems,
236
Sylow Subgroups of Subgroups,
238
Some Consequences of the Sylow Theorems,
239
When All Sylow Subgroups Are Normal,
240
When a Subgroup Acts Transitively; The Frattini Argument,
243
The Search for Simplicity,
244
Groups of Small Order,
250
On the Existence of Complements: The Schur-Zassenhaus Theorem,
252
*Sylow Subgroups of Sn,
258
Exercises,
261
9
The Classification Troblem for Groups,
263
The Classification Problem for Groups,
263
The Classification Problem for Finite Simple Groups,
263
Exercises,
271
10
Finiteness Conditions,
273
Groups with Operators,
273
Ω
-Series
and
Ω
-Subnormalìty,
276
Composition Series,
278
The Remak Decomposition,
282
Exercises,
288
11
Solvable and
Nüpotent
Groups,
291
Classes of Groups,
291
Operations on Series,
293
Closure Properties of Groups Defined by Series,
295
Nilpotent
Groups,
297
Solvability,
305
Exercises,
313
xii Contents
12
Free Groups and Presentations,
319
Ftee Groups,
319
Relatively Free Groups,
326
Presentations of a Group,
336
Exercises,
350
13
Abelian Groups,
353
An Abelian Group as a Z-Module,
355
The Classification of Finitely-Generated Abelian Groups,
3 55
Projectivity and the Right-Inverse Property,
357
Injectivity and the Left-Inverse Property,
359
Exercises,
363
References,
367
List of Symbols,
371
Index,
373
|
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| indexdate | 2024-07-10T00:14:58Z |
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| isbn | 9780817683009 |
| language | English |
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| publishDate | 2012 |
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| spelling | Roman, Steven Verfasser aut Fundamentals of group theory an advanced approach Steven Roman Boston Birkhäuser 2012 XII, 380 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8176-8301-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024815107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roman, Steven Fundamentals of group theory an advanced approach Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | Fundamentals of group theory an advanced approach |
| title_auth | Fundamentals of group theory an advanced approach |
| title_exact_search | Fundamentals of group theory an advanced approach |
| title_full | Fundamentals of group theory an advanced approach Steven Roman |
| title_fullStr | Fundamentals of group theory an advanced approach Steven Roman |
| title_full_unstemmed | Fundamentals of group theory an advanced approach Steven Roman |
| title_short | Fundamentals of group theory |
| title_sort | fundamentals of group theory an advanced approach |
| title_sub | an advanced approach |
| topic | Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Group theory Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024815107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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