Constructive recognition of classical groups in odd characteristic.

DOI10.1016/j.jalgebra.2009.04.028zbMath1181.20044OpenAlexW4213216172MaRDI QIDQ731248

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

Publication date: 2 October 2009

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.04.028

zbMATH Keywords

classical groupsconstructive recognitionLas Vegas algorithms

Mathematics Subject Classification ID

Related Items (20)

Proportions of elements with given 2-part order in finite classical groups of odd characteristic. ⋮ Gaussian elimination in unitary groups with an application to cryptography ⋮ A new method for recognising Suzuki groups ⋮ Recognising simplicity of black-box groups by constructing involutions and their centralisers. ⋮ On proportions of pre-involutions in finite classical groups. ⋮ Recognising the small Ree groups in their natural representations. ⋮ Presentations of finite simple groups: a computational approach. ⋮ Strong involutions in finite special linear groups of odd characteristic ⋮ Constructive recognition of classical groups in even characteristic. ⋮ The product replacement prospector. ⋮ Effective black-box constructive recognition of classical groups. ⋮ A practical model for computation with matrix groups. ⋮ On the twisted modules for finite matrix groups ⋮ Estimating proportions of elements in finite groups of Lie type. ⋮ Recognition of finite exceptional groups of Lie type ⋮ Involution centralisers in finite unitary groups of odd characteristic ⋮ Presentations on standard generators for classical groups ⋮ Large element orders and the characteristic of Lie-type simple groups. ⋮ Probabilistic generation of finite classical groups in odd characteristic by involutions ⋮ Regular semisimple elements and involutions in finite general linear groups of odd characteristic

Uses Software

• Magma

Cites Work

• Finding involutions in finite Lie type groups of odd characteristic.
• Fast algorithms for the characteristic polynomial
• Tensor products are projective geometries
• The Magma algebra system. I: The user language
• Constructive recognition of classical groups in their natural representation.
• An improved method for generating the centralizer of an involution
• The probability of generating a finite simple group
• Constructive recognition of \(\text{SL}_3(q)\).
• Recognising the Suzuki groups in their natural representations.
• Fast constructive recognition of black box orthogonal groups.
• Writing projective representations over subfields.
• On the spinor norm
• Black box classical groups
• Constructive membership in black-box groups
• A Recognition Algorithm For Classical Groups Over Finite Fields
• A black-box group algorithm for recognizing finite symmetric and alternating groups, I
• Fast Constructive Recognition of Black-Box Unitary Groups
• Generating random elements of a finite group
• Nearly Optimal Algorithms for Canonical Matrix Forms
• Endliche Gruppen I
• Constructive recognition of 𝑃𝑆𝐿(2,𝑞)
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