On deciding finiteness of matrix groups.

DOI10.1016/j.jsc.2009.02.001zbMath1172.20310OpenAlexW2101515171MaRDI QIDQ1023267

Dane L. Flannery, Alla S. Detinko

Publication date: 11 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2009.02.001

zbMATH Keywords

general linear groupsrecognition algorithmsexponential-time algorithmsfinitely generated matrix groupsfiniteness problemmatrix groups over function fields

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to group theory (20-04) Other matrix groups over fields (20H20)

Related Items (6)

Irreducibility testing of finite nilpotent linear groups. ⋮ Universality of single-qudit gates ⋮ The constructive membership problem for discrete two-generator subgroups of \(\operatorname{SL}_2(\mathbb{R})\) ⋮ Deciding finiteness of matrix groups in positive characteristic. ⋮ Linear groups and computation ⋮ Algorithms for the Tits alternative and related problems.

Uses Software

• GAP
• Magma
• Nilmat

Cites Work

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• Deciding finiteness for matrix groups over function fields
• The Magma algebra system. I: The user language
• Combinatorial group theory.
• Algorithms for computing with nilpotent matrix groups over infinite domains.
• On Deciding Finiteness for Matrix Groups over Fields of Positive Characteristic
• Maximal Abelian Subgroups of the Symmetric Groups
• Deciding finiteness for matrix semigroups over function fields over finite fields. A note on a paper by Rockmore, Tan, and Beals

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