A practical algorithm for finding matrix representations for polycyclic groups

DOI10.1006/jsco.1999.0286zbMath0977.20026OpenAlexW1988118972MaRDI QIDQ1974696

Eddie H. Lo, 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/c08002e461928c92e89f2416bfb4fe71dd76b54a

zbMATH Keywords

algorithmspolycyclic groupsfree nilpotent groupsfinite presentationsrepresentations by integer matrices

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) Nilpotent groups (20F18) 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 (6)

The status of polycyclic group-based cryptography: a survey and open problems ⋮ Minimal faithful representations of the free 2-step nilpotent Lie algebra of the rank \(r\) ⋮ Using the Mal'cev correspondence for collection in polycyclic groups. ⋮ On the dimension of matrix embeddings of torsion-free nilpotent groups ⋮ Algorithms for computing with nilpotent matrix groups over infinite domains. ⋮ Linear groups and computation

Cites Work

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• Some general algorithms. II: Nilpotent groups
• The algorithmic theory of polycyclic-by-finite groups
• Group rings and their augmentation ideals
• Finding intersections and normalizers in finitely generated nilpotent groups
• A polycyclic quotient algorithm
• Decidable Properties of Polycyclic Groups
• Finiteness Conditions for Soluble Groups

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