Decidable Properties of Polycyclic Groups

DOI10.1112/plms/s3-61.3.497zbMath0674.20020OpenAlexW2026950998MaRDI QIDQ3828191

Daniel Segal

Publication date: 1990

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-61.3.497

zbMATH Keywords

algorithmundecidabilitypolycyclic-by-finite groupsautomorphismHilbert's 10th problemisomorphism problemarithmetic groupconjugacy problemfinite presentationsconjugacy of subgroupsfinitely generated torsion-free nilpotent group

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Automorphisms of infinite groups (20E36) Linear algebraic groups over global fields and their integers (20G30) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (18)

Computing presentations for subgroups of polycyclic groups and of context-free groups ⋮ On rigidity and the isomorphism problem for tree braid groups. ⋮ Derivations and the permutability of subgroups in polycyclic-by-finite groups ⋮ The status of polycyclic group-based cryptography: a survey and open problems ⋮ Groups with Cyclic Outer Automizers ⋮ The isomorphism problem for finitely generated fully residually free groups. ⋮ Algorithmic recognition of infinite cyclic extensions ⋮ Positive elements and sufficient conditions for solvability of the submonoid membership problem for nilpotent groups of class two ⋮ Deciding isomorphy using Dehn fillings, the splitting case ⋮ The algorithmic theory of polycyclic-by-finite groups ⋮ A practical algorithm for finding matrix representations for polycyclic groups ⋮ Subgroup conjugacy separability of free-by-finite groups. ⋮ The isomorphism problem for all hyperbolic groups. ⋮ Algorithmic problems in Engel groups and cryptographic applications ⋮ The Algorithmic Theory of Finitely Generated Metabelian Groups ⋮ Generation of polycyclic groups ⋮ Surfaces of general type with geometric genus zero: a survey ⋮ The isomorphism problem for toral relatively hyperbolic groups.

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