Visual group theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington
Mathematical Association of America
[2009]
|
| Series: | Classroom resource materials
vol 32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 297 Seiten Illustrationen, Diagramme |
| ISBN: | 9780883857571 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Acknowledgments
vii
Preface
ix
Overview
1
1
What is a group?
3
1.1
A famous toy
............................... 3
1.2
Considering the cube
........................... 4
1.3
The study of symmetry
.......................... 5
1.4
Rules of a group
............................. 6
1.5
Exercises
................................. 7
2
What do groups look like?
11
2.1
Mapmaking
................................ 11
2.2
A not-so-famous toy
........................... 14
2.3
Mapping a group
............................. 15
2.4
Cayley diagrams
.............................. 18
2.5
A touch more abstract
.......................... 19
2.6
Exercises
................................. 21
3
Why study groups?
25
3.1
Groups of symmetries
........................... 25
3.2
Groups of actions
............................. 34
3.3
Groups everywhere
............................ 36
3.4
Exercises
................................. 37
4
Algebra at last
41
4.1
Where have all the actions gone?
.................... 41
4.2
Combine, combine, combine
....................... 44
4.3
Multiplication tables
........................... 45
4.4
The classic definition
............................ 48
4.5
Exercises
................................. 52
xi
xjj
Contents
5
Five families
63
5.1
Cyclic groups
............................... 64
5.2
Abelian groups
.............................. 68
5.3
Dihedral groups
..............................
74
5.4
Symmetric and alternating groups
.................... 78
5.5
Exercises
................................. 87
6
Subgroups
97
6.1
What multiplication tables say about Cayley diagrams
......... 97
6.2
Seeing subgroups
............................. 99
6.3
Revealing subgroups
........................... 101
6.4
Cosets
................................... 102
6.5
Lagrange s theorem
............................ 105
6.6
Exercises
................................. 108
7
Products and quotients
117
7.1
The direct product
............................ 117
7.2
Semidirect products
............................ 128
7.3
Normal subgroups and quotients
..................... 132
7.4
Normalizers
................................ 140
7.5
Conjugacy
................................. 142
7.6
Exercises
................................. 147
8
The power of homomorphisms
157
8.1
Embeddings and quotient maps
..................... 157
8.2
The Fundamental Homomorphism Theorem
............... 167
8.3
Modular arithmetic
............................ 169
8.4
Direct products and relatively prime numbers
.............. 172
8.5
The Fundamental Theorem of Abelian Groups
............. 175
8.6
Semidirect products revisited
....................... 177
8.7
Exercises
................................. 179
9
Sylow theory
193
9.1
Group actions
............................... 194
9.2
Approaching Sylow: Cauchy s Theorem
................. 199
9.3
p-groups
.................................. 205
9.4
Sylow Theorems
............................. 208
9.5
Exercises
................................. 217
10
Galois theory
221
10.1
The big question
............................. 221
10.2
More big questions
............................ 225
10.3
Visualizing field extensions
........................ 228
10.4
Irreducible polynomials
.......................... 231
10.5
Galois groups
............................... 233
10.6
The heart of Galois theory
........................ 243
10.7
Unsolvability
............................... 247
10.8
Exercises
................................. 252
Contents xiii
A Answers to selected Exercises
261
Bibliography
285
Index of Symbols Used
287
Index
289
About the Author
297
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| genre_facet | Einführung |
| id | DE-604.BV035644411 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:19Z |
| institution | BVB |
| isbn | 9780883857571 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017699144 |
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| physical | xiii, 297 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | Mathematical Association of America |
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| series | Classroom resource materials |
| series2 | Classroom resource materials |
| spelling | Carter, Nathan C. Verfasser (DE-588)139029230 aut Visual group theory Nathan C. Carter Washington Mathematical Association of America [2009] © 2009 xiii, 297 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Classroom resource materials vol 32 Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Gruppentheorie (DE-588)4072157-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-61444-102-1 Classroom resource materials vol 32 (DE-604)BV009530945 32 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017699144&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carter, Nathan C. Visual group theory Classroom resource materials Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4151278-9 |
| title | Visual group theory |
| title_auth | Visual group theory |
| title_exact_search | Visual group theory |
| title_full | Visual group theory Nathan C. Carter |
| title_fullStr | Visual group theory Nathan C. Carter |
| title_full_unstemmed | Visual group theory Nathan C. Carter |
| title_short | Visual group theory |
| title_sort | visual group theory |
| topic | Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Group theory Gruppentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017699144&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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