The use of permutation representations in structural computations in large finite matrix groups

DOI10.1016/j.jsc.2018.09.001zbMath1453.20001OpenAlexW2891478563MaRDI QIDQ2000260

John J. Cannon, William R. Unger, Derek F. Holt

Publication date: 28 June 2019

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

Full work available at URL: http://wrap.warwick.ac.uk/108208/13/WRAP-use-permutation-representations-structural-computations-matrix-Holt-2018.pdf

zbMATH Keywords

permutation representationfinite matrix groupstructural computation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Representation theory of groups (20C99) Other matrix groups over finite fields (20H30) Computational methods for problems pertaining to group theory (20-08)

Related Items (1)

SUBGROUPS WITH NO ABELIAN COMPOSITION FACTORS ARE NOT DISTINGUISHED

Uses Software

• GAP
• Magma
• matrixss
• recog
• ATLAS Group Representations

Cites Work

• A practical model for computation with matrix groups.
• Minimal degree for a permutation representation of a classical group
• Minimal permutation representations of finite simple classical groups. Special linear, symplectic, and unitary groups
• The Magma algebra system. I: The user language
• Selecting base points for the Schreier-Sims algorithm for matrix groups
• Minimal permutation representations of finite simple orthogonal groups
• Recognizing finite matrix groups over infinite fields.
• Computing conjugacy classes of elements in matrix groups.
• Computing subgroups of bounded index in a finite group.
• Computing the character table of a finite group.
• Computing maximal subgroups of finite groups.
• On the maximum orders of elements of finite almost simple groups and primitive permutation groups
• A data structure for a uniform approach to computations with finite groups
• On minimal faithful permutation representations of finite groups
• Reliability and reproducibility of Atlas information
• Polynomial-time theory of matrix groups
• On the Overgroups of Irreducible Subgroups of the Finite Classical Groups
• Computing the subgroups of a permutation group
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