Finiteness theorems for polycyclic groups

DOI10.1090/S0273-0979-1979-14630-5zbMath0408.20020MaRDI QIDQ4195128

P. F. Pickel, Fritz J. Grunewald, Daniel Segal

Publication date: 1979

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Polycyclic-By-Finite GroupsIsomorphism Classes of Finite Quotients of a GroupProfinite CompletionsSoluble-By-Finite Subconjugancy Classes

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) General structure theorems for groups (20E34) Chains and lattices of subgroups, subnormal subgroups (20E15) Linear algebraic groups over global fields and their integers (20G30) Residual properties and generalizations; residually finite groups (20E26) Limits, profinite groups (20E18)

Related Items (5)

The profinite completion of accessible groups ⋮ Profinite genus of free products with finite amalgamation ⋮ Profinite genus of the fundamental groups of compact flat manifolds with holonomy group of prime order ⋮ The genus of HNN-extensions ⋮ Topological groups

Cites Work

• The vanishing of certain homology and cohomology groups
• Fitting subgroups and profinite completions of polycyclic groups
• Two theorems on polycyclic groups
• Some finiteness properties of adele groups over number fields
• Théoremes de finitude en cohomologie galoisienne
• Structure of solvable Lie groups
• On polycyclic groups with isomorphic finite quotients
• A Note on Arithmetic Groups
• On congruence topologies in number fields.
• Nilpotent-By-Finite Groups With Isomorphic Finite Quotients
• Finitely Generated Nilpotent Groups with Isomorphic Finite Quotients

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