Products of Groups

Hardcover | April 30, 1999

byBernhard Amberg, Silvana Franciosi, Francesco de Giovanni

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Groups that are the product of two subgroups are of particular interest to group theorists. In what way is the structure of the product related to that of its subgroups? This monograph gives the first detailed account of the most important results that have been found about groups of this formover the past 35 years. Although the emphasis is on infinite groups, some relevant theorems about finite products of groups are also proved. The material presented will be of interest for research students and specialists in group theory. In particular, it can be used in seminars or to supplement ageneral group theory course. A special chapter on conjugacy and splitting theorems obtained by means of the cohomology of groups has never appeared in book form and should be of independent interest.

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Groups that are the product of two subgroups are of particular interest to group theorists. In what way is the structure of the product related to that of its subgroups? This monograph gives the first detailed account of the most important results that have been found about groups of this formover the past 35 years. Although the emphas...

Bernhard Amberg is at Johannes Gutenberg University, Mainz.
Format:HardcoverDimensions:232 pages, 9.21 × 6.14 × 0.75 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198535759

ISBN - 13:9780198535751

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Table of Contents

1. Elementary Properties of Factorized Groups1. The factorizer2. Normalizers, indices, and chain conditions3. Sylow subgroups4. Existence of factorizations2. Products of Nilpotent Groups5. Products of abelian groups6. Products of central-by-finite groups7. Residually finite products of abelian-by-finite groups8. The theorem of Kegel and Wielandt9. The structure of a finite product of nilpotent groups3. Products of Periodic Groups10. An example of a non-periodic product of two periodic groups11. Soluble products of periodic groups12. Soluble products of groups of finite exponent4. Products of Groups of Finite Rank13. Rank formulae14. The number of generators of a finite soluble group15. Factorized groups with finite Prufer rank16. Soluble products of polycyclic groups17. Products of a nilpotent and polycyclic group18. Soluble products of groups of finite rank5. Splitting and Conjugacy Theorems19. Cohomology of groups20. Cohomological machinery21. Splitting and conjugacy22. Near splitting and near conjugacy6. Triply Factorized Groups23. Examples of groups with an abelian triple factorization24. Lower central factors and tensor products25. Groups with a nilpotent triple factorization26. FC-nilpotent and FC-hypercentral groups27. Groups with a supersoluble triple factorization28. Trifactorized groups7. Some Further Topics29. The 'inside-outside' problem30. The fitting length of a soluble product of nilpotent groups31. Products of an abelian and an FC-group32. Products of locally cyclic groups33. Subnormal subgroups of factorized groups34. Groups factorized by finitely many subgroups35. BibliographyIndex

Editorial Reviews

`The authors have performed a useful service in bringing together this material. The text is well and clearly written and it contains very complete references to the literature and a number of open questions. The book would therefore form an admirable and stimulating introduction for a studentcontemplating research in the area. The mathematical community should be grateful to the authors for this account of a challenging subject which has developed rapidly in the last forty years but in which some very natural questions still remain open.'John S. Wilson, Mathematical Reviews