Constructive membership in black-box groups

DOI10.1515/JGT.2008.047zbMath1173.20036OpenAlexW1976647207MaRDI QIDQ3544292

Petra E. Holmes, Robert A. Wilson, E. A. O'Brien, Stephen A. Linton, Alexander J. E. Ryba

Publication date: 5 December 2008

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

Full work available at URL: https://doi.org/10.1515/jgt.2008.047

zbMATH Keywords

Monte Carlo algorithmsrandom elementspolynomial time algorithmsfinite simple groups of Lie typeblack-box groupsconstructive membership problemgroup-theoretic algorithmsmatrix groups over finite fields

Mathematics Subject Classification ID

Related Items (14)

Recognising simplicity of black-box groups by constructing involutions and their centralisers. ⋮ On proportions of pre-involutions in finite classical groups. ⋮ A note on computing involution centralizers. ⋮ Recognising the small Ree groups in their natural representations. ⋮ Constructing composition factors for a linear group in polynomial time ⋮ Strong involutions in finite special linear groups of odd characteristic ⋮ A practical model for computation with matrix groups. ⋮ Finite Groups and Complexity Theory: From Leningrad to Saint Petersburg via Las Vegas ⋮ Fast constructive recognition of black box symplectic groups. ⋮ Classification of subgroups isomorphic to in the Monster ⋮ Finding 47:23 in the Baby Monster ⋮ Constructive recognition of classical groups in odd characteristic. ⋮ Regular semisimple elements and involutions in finite general linear groups of odd characteristic ⋮ Black box exceptional groups of Lie type

Cites Work

• The Magma algebra system. I: The user language
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• On the probability that a group element is \(p\)-singular
• The probability of generating a finite simple group
• Fast constructive recognition of black box orthogonal groups.
• A Recognition Algorithm For Classical Groups Over Finite Fields
• Ru< E₇(5)
• Black-box recognition of finite simple groups of Lie type by statistics of element orders
• A black-box group algorithm for recognizing finite symmetric and alternating groups, I
• Generating random elements of a finite group
• Finding the characteristic of a group of Lie type
• Constructive recognition of 𝑃𝑆𝐿(2,𝑞)

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