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Zusatztext 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. Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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 ...
