Practical algorithms for polycyclic matrix groups

DOI10.1006/jsco.1999.0287zbMath0977.20024OpenAlexW2072901418MaRDI QIDQ1974695

Gretchen Ostheimer

Publication date: 8 May 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/657003b8ec200613b12d6a7252b35bb14ac244e8

zbMATH Keywords

algorithmspolycyclic matrix groupssubgroups of \(\text{GL}(n,\mathbb{Z})\)

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Solvable groups, supersolvable groups (20F16) Representation theory for linear algebraic groups (20G05) Generators, relations, and presentations of groups (20F05) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (10)

On the orbit-stabilizer problem for integral matrix actions of polycyclic groups ⋮ Computing polycyclic presentations for polycyclic rational matrix groups. ⋮ Algorithms for computing with nilpotent matrix groups over infinite domains. ⋮ On the Fitting subgroup of a polycyclic-by-finite group and its applications ⋮ Linear groups and computation ⋮ Algorithms for the Tits alternative and related problems. ⋮ Computing in Nilpotent Matrix Groups ⋮ Testing polycyclicity of finitely generated rational matrix groups ⋮ Orbit-stabilizer problems and computing normalizers for polycyclic groups. ⋮ The constructive membership problem for discrete free subgroups of rank 2 of

Cites Work

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• The algorithmic theory of polycyclic-by-finite groups
• Direct methods for primary decomposition
• On a question of Lehmer and the number of irreducible factors of a polynomial
• The Orbit-Stabilizer Problem for Linear Groups
• Computing a lattice basis from a system of generating vectors
• Maximal Abelian Subgroups of the Symmetric Groups

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