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.
PART 1: Elementary Properties of Factorized Groups 1. The Factorizer 2. Normalizers, Indices, and Chain Conditions 3. Sylow Subgroups 4. Existence of Factorizations PART II: 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 PART III: 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 PART IV: Products of Groups of Finite Rank 13. Rank Formulae 14. The Number of Generators of a Finite Soluble Group 15. Factorized Groups with Finite Pr?fer Rank 16. Soluble Products of Polycyclic Groups 17. Products of a Nilpotent and Polycyclic Group 18. Soluble Products of Groups of Finite Rank PART V: Splitting and Conjugacy Theorems 19. Cohomology of Groups 20. Cohomological Machinery 21. Splitting and Conjugacy 22. Near Splitting and Near Conjugacy PART VI: TriplC"
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