Recognising simplicity of black-box groups by constructing involutions and their centralisers.

DOI10.1016/j.jalgebra.2010.05.013zbMath1208.20045OpenAlexW1973520489MaRDI QIDQ606645

Robert A. Wilson, Christopher Parker

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.2010.05.013

zbMATH Keywords

involutionsfinite groups of Lie typeblack-box groupscomputational 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 (15)

Adjoint representations of black box groups \(\operatorname{PSL}_2(\mathbb{F}_q)\) ⋮ On proportions of pre-involutions in finite classical groups. ⋮ A note on computing involution centralizers. ⋮ Strong involutions in finite special linear groups of odd characteristic ⋮ Constructive recognition of classical groups in even characteristic. ⋮ On products of involutions in finite groups of Lie type in even characteristic. ⋮ Effective black-box constructive recognition of classical groups. ⋮ Black box exceptional groups of Lie type. II. ⋮ Recognition of finite exceptional groups of Lie type ⋮ Involution centralisers in finite unitary groups of odd characteristic ⋮ Odd order products of conjugate involutions in linear groups over \(\mathrm{GF}(2^a)\) ⋮ A note on involution centralizers in black box 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 ⋮ Black box exceptional groups of Lie type

Cites Work

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