On proportions of pre-involutions in finite classical groups.

DOI10.1016/j.jalgebra.2010.03.026zbMath1208.20044OpenAlexW2036860053WikidataQ56987675 ScholiaQ56987675MaRDI QIDQ606652

Alice C. Niemeyer, Cheryl E. Praeger, Tomasz Popiel

Publication date: 18 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.03.026

zbMATH Keywords

involutionsfinite groups of Lie typerecognition algorithmsfinite classical groupsblack-box groupsproportionscomputational group theory

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear algebraic groups over finite fields (20G40) Software, source code, etc. for problems pertaining to group theory (20-04) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (5)

Recognising simplicity of black-box groups by constructing involutions and their centralisers. ⋮ Abundant \(p\)-singular elements in finite classical groups. ⋮ A semi-recursion for the number of involutions in special orthogonal groups over finite fields ⋮ Convergence criteria for \(\text{FI}_{\mathcal{W}}\)-algebras and polynomial statistics on maximal tori in type B/C ⋮ Estimating proportions of elements in finite groups of Lie type.

Cites Work

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• Recognising simplicity of black-box groups by constructing involutions and their centralisers.
• Constructive recognition of classical groups in odd characteristic.
• Finding involutions in finite Lie type groups of odd characteristic.
• Estimating proportions of elements in finite groups of Lie type.
• Permutation groups and derangements of odd prime order
• Constructive membership in black-box groups
• Linear algebraic groups.

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