The Orbit-Stabilizer Problem for Linear Groups

DOI10.4153/CJM-1985-015-4zbMath0552.20019MaRDI QIDQ3344120

John D. Dixon

Publication date: 1985

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

complexityalgorithmsgeneratorsorbit problemfinitely generated group of matricesnilpotent by finite groupsstabilizer problem

Mathematics Subject Classification ID

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)

Related Items (13)

On the orbit-stabilizer problem for integral matrix actions of polycyclic groups ⋮ On the Frattini subgroup of a polycyclic group ⋮ Algorithms for linear groups of finite rank. ⋮ Algorithms for arithmetic groups with the congruence subgroup property. ⋮ Integrality and arithmeticity of solvable linear groups. ⋮ Computing polycyclic presentations for polycyclic rational matrix groups. ⋮ Practical algorithms for polycyclic matrix groups ⋮ Algorithms for computing with nilpotent matrix groups over infinite domains. ⋮ Conditions for linear groups to have unipotent derived subgroups. ⋮ 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. ⋮ Orbit-stabilizer problems and computing normalizers for polycyclic groups.

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