Probabilistic generation of finite classical groups in odd characteristic by involutions

DOI10.1515/JGT.2010.061zbMath1244.20044WikidataQ56987654 ScholiaQ56987654MaRDI QIDQ3096073

Seress, Ákos, Cheryl E. Praeger

Publication date: 7 November 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

zbMATH Keywords

randomized algorithmsfinite classical groupsgeneralized Fitting subgrouprandom involutionsprobabilistic generationbalanced involutionsconstructive recognition algorithms

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Special subgroups (Frattini, Fitting, etc.) (20D25) Generators, relations, and presentations of groups (20F05) Simple groups: alternating groups and groups of Lie type (20D06) Probabilistic methods in group theory (20P05)

Related Items (5)

A note on computing involution centralizers. ⋮ Strong involutions in finite special linear groups of odd characteristic ⋮ Generation of finite classical groups by pairs of elements with large fixed point spaces. ⋮ Involution centralisers in finite unitary groups of odd characteristic ⋮ Regular semisimple elements and involutions in finite general linear groups of odd characteristic

Cites Work

• Recognising simplicity of black-box groups by constructing involutions and their centralisers.
• Constructive recognition of classical groups in odd characteristic.
• On the maximal subgroups of the finite classical groups
• Fixed point ratios in actions of finite classical groups. I.
• Fixed point ratios in actions of finite classical groups. II.
• Classical groups, probabilistic methods, and the \((2,3)\)-generation problem
• Fixed point ratios in actions of finite classical groups. III.
• Fixed point ratios in actions of finite classical groups. IV.
• The probability of generating a finite classical group
• RANDOM (r, s)-GENERATION OF FINITE CLASSICAL GROUPS
• On the Random Generation of Finite Simple Classical Groups
• On the Orders of Maximal Subgroups of the Finite Classical Groups

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