A course in the theory of groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY u.a.
Springer
1993
|
| Schriftenreihe: | Graduate texts in mathematics
80 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 481 S. graph. Darst. |
| ISBN: | 0387906002 3540906002 0387940928 3540940928 |
Internformat
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| 100 | 1 | |a Robinson, Derek John Scott |d 1938- |e Verfasser |0 (DE-588)1017969213 |4 aut | |
| 245 | 1 | 0 | |a A course in the theory of groups |c Derek J. S. Robinson |
| 264 | 1 | |a New York, NY u.a. |b Springer |c 1993 | |
| 300 | |a XVII, 481 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 80 | |
| 650 | 4 | |a Groupes, Théorie des | |
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Datensatz im Suchindex
| _version_ | 1805066982477791232 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
NOTATION
XV
CHAPTER
1
FUNDAMENTAL
CONCEPTS
OF
GROUP
THEORY
1
1.1
BINARY
OPERATION,
SEMIGROUPS,
AND
GROUPS
1
1.2
EXAMPLES
OF
GROUPS
4
1.3
SUBGROUPS
AND
COSETS
7
1.4
HOMOMORPHISMS
AND
QUOTIENT
GROUPS
17
1.5
ENDOMORPHISMS
AND
AUTOMORPHISMS
25
1.6
PERMUTATION
GROUPS
AND
GROUP
ACTIONS
31
CHAPTER
2
FREE
GROUPS
AND
PRESENTATIONS
44
2.1
FREE
GROUPS
44
2.2
PRESENTATIONS
OF
GROUPS
50
2.3
VARIETIES
OF
GROUPS
54
CHAPTER
3
DECOMPOSITIONS
OF
A
GROUP
61
3.1
SERIES
AND
COMPOSITION
SERIES
61
3.2
SOME
SIMPLE
GROUPS
69
3.3
DIRECT
DECOMPOSITIONS
77
CHAPTER
4
ABELIAN
GROUPS
90
4.1
TORSION
GROUPS
AND
DIVISIBLE
GROUPS
90
4.2
DIRECT
SUMS
OF
CYCLIC
AND
QUASICYCLIC
GROUPS
95
XI
XII
CONTENTS
4.3
PURE
SUBGROUPS
AND
P-GROUPS
102
4.4
TORSION-FREE
GROUPS
111
CHAPTER
5
SOLUBLE
AND
NILPOTENT
GROUPS
117
5.1
ABELIAN
AND
CENTRAL
SERIES
117
5.2
NILPOTENT
GROUPS
125
5.3
GROUPS
OF
PRIME-POWER
ORDER
135
5.4
SOLUBLE
GROUPS
142
CHAPTER
6
FREE
GROUPS
AND
FREE
PRODUCTS
153
6.1
FUERTHER
PROPERTIES
OF
FREE
GROUPS
153
6.2
FREE
PRODUCTS
OF
GROUPS
161
6.3
SUBGROUPS
OF
FREE
PRODUCTS
167
6.4
GENERALIZED
FREE
PRODUCTS
177
CHAPTER
7
FINITE
PERMUTATION
GROUPS
185
7.1
MULTIPLE
TRANSITIVITY
185
7.2
PRIMITIVE
PERMUTATION
GROUPS
190
7.3
CLASSIFICATION
OF
SHARPLY
K
TRANSITIVE
PERMUTATION
GROUPS
196
7.4
THE
MATHIEU
GROUPS
201
CHAPTER
8
REPRESENTATIONS
OF
GROUPS
206
8.1
REPRESENTATIONS
AND
MODULES
206
8.2
STRUCTURE
OF
THE
GROUP
ALGEBRA
215
8.3
CHARACTERS
219
8.4
TENSOR
PRODUCTS
AND
REPRESENTATIONS
228
8.5
APPLICATIONS
TO
FINITE
GROUPS
239
CHAPTER
9
FINITE
SOLUBLE
GROUPS
245
9.1
HALL
TR-SUBGROUPS
245
9.2
SYLOW
SYSTEMS
AND
SYSTEM
NORMALIZERS
254
9.3
P-SOLUBLE
GROUPS
261
9.4
SUPERSOLUBLE
GROUPS
266
9.5
FORMATIONS
269
CONTENTS
XIII
CHAPTER
10
THE
TRANSFER
AND
ITS
APPLICATIONS
276
10.1
THE
TRANSFER
HOMOMORPHISM
276
10.2
GRUEN
'
S
THEOREMS
283
10.3
FROBENIUS
'
CRITERION
FOR
P-NILPOTENCE
286
10.4
THOMPSON
'
S
CRITERION
FOR
P-NILPOTENCE
289
10.5
FIXED-POINT-FREE
AUTOMORPHISMS
295
CHAPTER
11
THE
THEORY
OF
GROUP
EXTENSIONS
301
11.1
GROUP
EXTENSIONS
AND
COVERING
GROUPS
301
11.2
HOMOLOGY
GROUPS
AND
COHOMOLOGY
GROUPS
313
11.3
THE
GRUENBERG
RESOLUTION
320
11.4
GROUP-THEORETIC
INTERPRETATIONS
OF
THE
(CO)HOMOLOGY
GROUPS
328
CHAPTER
12
GENERALIZATIONS
OF
NILPOTENT
AND
SOLUBLE
GROUPS
342
12.1
LOCALLY
NILPOTENT
GROUPS
342
12.2
SOME
SPECIAL
TYPES
OF
LOCALLY
NILPOTENT
GROUPS
350
12.3
ENGEL
ELEMENTS
AND
ENGEL
GROUPS
355
12.4
CLASSES
OF
GROUPS
DEFINED
BY
GENERAL
SERIES
362
12.5
LOCALLY
SOLUBLE
GROUPS
367
CHAPTER
13
SUBNORMAL
SUBGROUPS
371
13.1
JOINS
AND
INTERSECTIONS
OF
SUBNORMAL
SUBGROUPS
371
13.2
PERMUTABILITY
AND
SUBNORMALITY
379
13.3
THE
MINIMAL
CONDITION
ON
SUBNORMAL
SUBGROUPS
382
13.4
GROUPS
IN
WHICH
NORMALITY
IS
A
TRANSITIVE
RELATION
388
13.5
AUTOMORPHISM
TOWERS
AND
COMPLETE
GROUPS
394
CHAPTER
14
FINITENESS
PROPERTIES
401
14.1
FINITELY
GENERATED
GROUPS
AND
FINITELY
PRESENTED
GROUPS
401
14.2
TORSION
GROUPS
AND
THE
BURNSIDE
PROBLEMS
407
14.3
LOCALLY
FINITE
GROUPS
411
14.4
2-GROUPS
WITH
THE
MAXIMAL
OR
MINIMAL
CONDITION
419
14.5
FINITENESS
PROPERTIES
OF
CONJUGATES
AND
COMMUTATORS
422
XIV
CONTENTS
CHAPTER
15
INFINITE
SOLUBLE
GROUPS
433
15.1
SOLUBLE
LINEAR
GROUPS
433
15.2
SOLUBLE
GROUPS
WITH
FINITENESS
CONDITIONS
ON
ABELIAN
SUBGROUPS
438
15.3
FINITELY
GENERATED
SOLUBLE
GROUPS
AND
THE
MAXIMAL
CONDITION
ON
NORMAL
SUBGROUPS
444
15.4
FINITELY
GENERATED
SOLUBLE
GROUPS
AND
RESIDUAL
FINITENESS
453
15.5
FINITELY
GENERATED
SOLUBLE
GROUPS
AND
THEIR
FRATTINI
SUBGROUPS
457
BIBLIOGRAPHY
461
INDEX
472 |
| any_adam_object | 1 |
| author | Robinson, Derek John Scott 1938- |
| author_GND | (DE-588)1017969213 |
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| callnumber-raw | QA174.2.R63 1993 |
| callnumber-search | QA174.2.R63 1993 |
| callnumber-sort | QA 3174.2 R63 41993 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| classification_tum | MAT 200f |
| ctrlnum | (OCoLC)28798205 (DE-599)BVBBV009569030 |
| dewey-full | 512/.2 512/.220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 512/.2 20 |
| dewey-search | 512/.2 512/.2 20 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T03:26:59Z |
| institution | BVB |
| isbn | 0387906002 3540906002 0387940928 3540940928 |
| language | English |
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| physical | XVII, 481 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Robinson, Derek John Scott 1938- Verfasser (DE-588)1017969213 aut A course in the theory of groups Derek J. S. Robinson New York, NY u.a. Springer 1993 XVII, 481 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 80 Groupes, Théorie des Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Graduate texts in mathematics 80 (DE-604)BV000000067 80 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006321841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robinson, Derek John Scott 1938- A course in the theory of groups Graduate texts in mathematics Groupes, Théorie des Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | A course in the theory of groups |
| title_auth | A course in the theory of groups |
| title_exact_search | A course in the theory of groups |
| title_full | A course in the theory of groups Derek J. S. Robinson |
| title_fullStr | A course in the theory of groups Derek J. S. Robinson |
| title_full_unstemmed | A course in the theory of groups Derek J. S. Robinson |
| title_short | A course in the theory of groups |
| title_sort | a course in the theory of groups |
| topic | Groupes, Théorie des Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Groupes, Théorie des Group theory Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006321841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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