Overview

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 form over 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 a general 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.

Full Product Details

Author:   Bernhard Amberg (Professor, Professor, Johannes Gutenberg University, Mainz) ,  Silvana Franciosi ,  Francesco de Giovanni (both Professors a, both Professors a, University of Naples, Italy) ,  Francesco de Giovanni (Professor, University of Naples, Italy)
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Dimensions:   Width: 16.00cm , Height: 1.90cm , Length: 24.10cm
Weight:   0.510kg
ISBN:  

9780198535751

ISBN 10:   0198535759
Pages:   232
Publication Date:   28 January 1993
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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 Prufer 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

Reviews

'This monograph gives the first detailed account of the most important results that have been found about the groups that are the product of two subgroups.' L'Enseignement MathDematique, 3-4, 1993 'This book is a good source for anyone who wants to know about the situation in this area; the systematic arrangement eases the task for someone who looks for a particular result of Chernikov, Kazarin, Zaitsev and the authors - to mention only those contributors who are mentioned more than six times in the bibliography of around 170 entries.' H. Heineken, Zbl. Math. 774 - 9 `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 student contemplating 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

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 be an admirable and stimulating introduction for a student contemplating research in the area. . . . The mathematical community should be grateful to the authors for this account of a challenging subject. . . --Mathematical Review<br>

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 be an admirable and stimulating introduction for a student contemplating research in the area. . . . The mathematical community should be grateful to the authors for this account of a challenging subject. . . --Mathematical Review

<br> 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 be an admirable and stimulating introduction for a student contemplating research in the area. . . . The mathematical community should be grateful to the authors for this account of a challenging subject. . . --Mathematical Review<p><br>

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