Products of Groups

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