Constructive recognition of 𝑃𝑆𝐿(2,𝑞)

DOI10.1090/S0002-9947-05-03756-6zbMath1105.20013OpenAlexW1495167062MaRDI QIDQ5713172

E. A. O'Brien, Marston D. E. Conder, Charles R. Leedham-Green

Publication date: 12 December 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03756-6

zbMATH Keywords

polynomial time algorithmsefficient algorithmslinear groups over finite fieldsconstructive recognitionrandomised algorithmsPSL

Mathematics Subject Classification ID

Related Items (17)

Recognising the small Ree groups in their natural representations. ⋮ Constructing composition factors for a linear group in polynomial time ⋮ Constructive recognition of classical groups in even characteristic. ⋮ Black box groups isomorphic to \(\mathrm{PGL}(2,2^e)\). ⋮ Effective black-box constructive recognition of classical groups. ⋮ Black box exceptional groups of Lie type. II. ⋮ Constructive membership in black-box groups ⋮ A practical model for computation with matrix groups. ⋮ Constructive recognition of \(\text{SL}_3(q)\). ⋮ Finite Groups and Complexity Theory: From Leningrad to Saint Petersburg via Las Vegas ⋮ Fast constructive recognition of black box symplectic groups. ⋮ Recognising the Suzuki groups in their natural representations. ⋮ Fast constructive recognition of black box orthogonal groups. ⋮ Recognition of finite exceptional groups of Lie type ⋮ Constructive recognition of classical groups in odd characteristic. ⋮ Computing a Chief Series and the Soluble Radical of a Matrix Group Over a Finite Field ⋮ Black box exceptional groups of Lie type

Uses Software

• Magma
• MeatAxe

Cites Work

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• Tensor products are projective geometries
• Short presentations for finite groups
• The Magma algebra system. I: The user language
• Constructive recognition of classical groups in their natural representation.
• Fast Monte Carlo algorithms for permutation groups
• On the modular characters of groups
• Black box classical groups
• Writing representations over minimal fields
• Recognising Tensor Products of Matrix Groups
• Treating the Exceptional Cases of the MeatAxe
• Black-box recognition of finite simple groups of Lie type by statistics of element orders
• Generating random elements of a finite group
• A Second Note on the Linear Fractional Group
• Short presentations for three-dimensional unitary groups.

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