Bernhard Amberg, Silvana Franciosi, Francesco De Giovanni

Products of Groups

• Gebundenes Buch

Produktbeschreibung

Groups comprising two subcomponents are of particular interest to group theorists who want to know in what way the structure of the product is related to that of its subgroups. This monograph gives the first detailed account of the most important results of group product research from the past 35 years. Although the emphasis is on infinite groups, relevant theorems about finite products of groups are also proved. This book will be of interest to research students and specialists in group theory, and will be useful in seminars or as a supplement in courses in general group theory. A special chapter on conjugacy and splitting theorems obtained by means of the cohomology of groups has never before appeared in book form.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 232
• Erscheinungstermin: 25. Februar 1993
• Englisch
• Abmessung: 229mm x 152mm x 18mm
• Gewicht: 517g
• ISBN-13: 9780198535751
• ISBN-10: 0198535759
• Artikelnr.: 21981205

Inhaltsangabe

1. Elementary Properties of Factorized Groups
1: The factorizer
2: Normalizers, indices, and chain conditions
3: Sylow subgroups
4: Existence of factorizations
2. Products of Nilpotent Groups
5: Products of abelian groups
6: Products of central-by-finite groups
7: Residually finite products of abelian-by-finite groups
8: The theorem of Kegel and Wielandt
9: The structure of a finite product of nilpotent groups
3. Products of Periodic Groups
10: An example of a non-periodic product of two periodic groups
11: Soluble products of periodic groups
12: Soluble products of groups of finite exponent
4. Products of Groups of Finite Rank
13: Rank formulae
14: The number of generators of a finite soluble group
15: Factorized groups with finite Prüfer rank
16: Soluble products of polycyclic groups
17: Products of a nilpotent and polycyclic group
18: Soluble products of groups of finite rank
5. Splitting and Conjugacy Theorems
19: Cohomology of groups
20: Cohomological machinery
21: Splitting and conjugacy
22: Near splitting and near conjugacy
6. Triply Factorized Groups
23: Examples of groups with an abelian triple factorization
24: Lower central factors and tensor products
25: Groups with a nilpotent triple factorization
26: FC-nilpotent and FC-hypercentral groups
27: Groups with a supersoluble triple factorization
28: Trifactorized groups
7. Some Further Topics
29: The 'inside-outside' problem
30: The fitting length of a soluble product of nilpotent groups
31: Products of an abelian and an FC-group
32: Products of locally cyclic groups
33: Subnormal subgroups of factorized groups
34: Groups factorized by finitely many subgroups
35: Bibliography
Index