On the orbit-stabilizer problem for integral matrix actions of polycyclic groups

DOI10.1090/S0025-5718-03-01493-5zbMath1051.20016OpenAlexW2030372221MaRDI QIDQ4806402

Gretchen Ostheimer, Bettina Eick

Publication date: 14 May 2003

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01493-5

zbMATH Keywords

algorithmspolycyclic groupsconjugacy problem

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Subgroup theorems; subgroup growth (20E07) Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) 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) Other matrix groups over fields (20H20)

Related Items (9)

The status of polycyclic group-based cryptography: a survey and open problems ⋮ A nonlinear decomposition attack ⋮ Algorithms for arithmetic groups with the congruence subgroup property. ⋮ Computing polycyclic presentations for polycyclic rational matrix groups. ⋮ Unnamed Item ⋮ Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem ⋮ ON THE CONJUGACY PROBLEM IN CERTAIN METABELIAN GROUPS ⋮ Computing in Nilpotent Matrix Groups ⋮ A family of polycyclic groups over which the uniform conjugacy problem is NP-complete

Uses Software

• GAP
• KANT/KASH
• Polycyclic
• AClib

Cites Work

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• Computing the Schur multiplicator and the nonabelian tensor square of a polycyclic group.
• The algorithmic theory of polycyclic-by-finite groups
• Fundamental algorithms for permutation groups
• KANT V4
• A polycyclic quotient algorithm
• Practical algorithms for polycyclic matrix groups
• Almost-Bieberbach groups: affine and polynomial structures
• The Orbit-Stabilizer Problem for Linear Groups

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