A course on finite groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2009
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 311 Seiten Diagramme |
| ISBN: | 9781848828889 |
Staff View
MARC
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| 100 | 1 | |a Rose, H.E. |d 1936- |0 (DE-588)1089506872 |4 aut | |
| 245 | 1 | 0 | |a A course on finite groups |c H. E. Rose |
| 264 | 1 | |a London |b Springer |c 2009 | |
| 300 | |a xii, 311 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Finite groups | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020195489 | ||
Record in the Search Index
| _version_ | 1804142783541280768 |
|---|---|
| adam_text | Contents
1
Introduction
—
The Group Concept
2
Elementary Group Properties
......................
II
2.1
Basic Definitions
........................... 11
2.2
Examples
............................... 17
2.3
Subgroups.
Coseis
and Lagrange s Theorem
............ 24
2.4
Normal Subgroups
.......................... 30
2.5
Problems
............................... 34
3
(¡roup
Construction and Representation
................ 41
3.1
Permutations
............................. 42
3.2
Permutation Groups
......................... 48
3.3
Malrix Groups
............................ 52
3.4
Group Presentation
.......................... 55
3.5
Problems
............................... 59
4
Homomorphisms
............................. 67
4.1
Homomorphisms and Isomorphisms
................ 69
4.2
Isomorphism Theorems
....................... 74
4.3
Cyclic Groups
............................ 79
4.4
Automorphism Groups
.......................
HI
4.5
Problems
...............................
X4
5
Action and the Orbit-Stabiliser Theorem
............... 91
5.1
Actions
................................ 92
5.2
Three Important Examples
...................... 99
5.3
Problems
............................... 107
6
^-Groups and Sylow Theory
....................... 113
6.1
Finite /»-Groups
...........................
I
14
6.2
Sylow Theory
............................ 119
6.3
Applications
............................. 126
6.4
Problems
............................... 131
x
Contents
7
Products and Abelian
Groups
...................... 139
7.1
Direct Products
............................ 140
7.2
Finite
Abelian
Groups........................
146
7.3
Semi-direct Products
......................... 151
7.4
Problems
............................... 159
8
Groups of Order
24,
Three Examples
..................
1
65
8.1
Symmetric Group
5д
......................... 165
8.2
Special Linear Group 5b(3)
.................... 172
8.3
Exceptional Group
E
........................ 177
8.4
Problems
............................... 183
9
Series, Jordan-Holder Theorem and the Extension Problem
..... 187
9.1
Composition Series and the Jordan-Holder Theorem
........ 188
9.2
Extension Problem
.......................... 196
9.3
Problems
............................... 205
10
Nilpotcncy
................................. 209
10.
1
Nilpotent
Groups
........................... 210
10.2
Fruttini
und
Fitting Subgroups
.................... 217
10.3
Problems
............................... 223
11
Solubility
................................. 229
11.1
Soluble Groups
........................... 230
11.2
Hall s Theorems and Solubility Conditions
............. 236
11.3
Problems
............................... 243
12
Simple Groups of Order Less than
10000................ 249
12.1 Steiner
Systems
........................... 250
12.2
Linear Groups
............................ 254
12.3
Unitary Groups
............................ 265
12.4
Mathieu
Groups
........................... 267
12.5
Problems
............................... 270
Appendices A to
E
............................... 277
A Set Theory
.............................. 277
В
Number Theory
........................... 284
С
Datu
on Groups of Order
24..................... 289
D
Numbers of Groups with Order up to
520.............. 293
К
Representations of
£2(4)
with Order
< 10000........... 295
Bibliography
.................................. 297
Notation Index
................................. 301
1—
Symbol Index
.......................... 301
2—
Notation for Classes of Groups
................. 303
3—
Notation for Individual Groups
................. 304
Index
...................................... 305
Web Contents
3
Group Construction and Representation
................32
1
3.6
Representations of
Л5
3.7
Further Problems
4
Homomorphisms
.............................331
4.6
The Transfer
4.7
Group Presentation. Part
2
4.X Further Problems
5
Action and the Orbit-Stabiliser Theorem
...............35
1
5.4
Transitive and Primitive Permutation Groups
5.5
Further Problems
6
p-Groups and Sylow Theory
.......................361
6.5
Applications
2—
Burnside s Normal Complement Theorem
and Groups with Cyclic Sylow Subgroups
6.6
Further Problems
7
Products and Abelian Groups
......................371
7.5
Infinite Abelian Groups
—
A Brief Introduction
9
Series, Jordan-Holder Theorem and the Extension Problem
374
9.4
Schur-Zassenhaus Theorem
9.5
Further Problems
12
Simple Groups of Order Less than
10000
3S7
12.6
Simple Groups of Order Less than lOOOOOO. Iwasavva s Lemma
and a Method for generating
Steiner
Systems tor some
Mathieu
Groups
12.7
Further Problems
13
Representation and Character Theory
401
13.1
Representations and Modules
xji
Web Contenls
13.2
Theorems of
Schur
and
Maschke
13.3
Characters and Orthogonality Relations
13.4
Lifts and Normal Subgroups
13.5
Problems
14
Character Tables and Theorems of Burnside and Frobenius
.....433
14.1
Character Tables
14.2
Burnside s prqs -Theorem
14.3
Frobenius Groups
14.4
Problems
Solution Appendix
—
Answers and Solutions,
Problems
2
to
12,
A and
В
........................ 461
Problem
2 .............................. 461
Problem
3 .............................. 472
Problem
4 .............................. 4SI
Problem
5 .............................. 4X9
Problem
6.............................. 497
Problem
7 .............................. 508
Problem
8 .............................. 515
Problem9
.............................. 521
Problem
10.............................. 524
Problem II
.............................. 532
Problem
12..............................
53X
Problem A
.............................. 544
Problem
В
.............................. 545
|
| any_adam_object | 1 |
| author | Rose, H.E. 1936- |
| author_GND | (DE-588)1089506872 |
| author_facet | Rose, H.E. 1936- |
| author_role | aut |
| author_sort | Rose, H.E. 1936- |
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| ctrlnum | (OCoLC)502402024 (DE-599)BVBBV025599950 |
| dewey-full | 512.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.23 |
| dewey-search | 512.23 |
| dewey-sort | 3512.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV025599950 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:37:15Z |
| institution | BVB |
| isbn | 9781848828889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020195489 |
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| physical | xii, 311 Seiten Diagramme |
| publishDate | 2009 |
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| series2 | Universitext |
| spelling | Rose, H.E. 1936- (DE-588)1089506872 aut A course on finite groups H. E. Rose London Springer 2009 xii, 311 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Universitext Finite groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Endliche Gruppe (DE-588)4014651-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-84882-889-6 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rose, H.E. 1936- A course on finite groups Finite groups Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4151278-9 |
| title | A course on finite groups |
| title_auth | A course on finite groups |
| title_exact_search | A course on finite groups |
| title_full | A course on finite groups H. E. Rose |
| title_fullStr | A course on finite groups H. E. Rose |
| title_full_unstemmed | A course on finite groups H. E. Rose |
| title_short | A course on finite groups |
| title_sort | a course on finite groups |
| topic | Finite groups Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Finite groups Endliche Gruppe Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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