Presentations of finite simple groups: A quantitative approach

DOI10.1090/S0894-0347-08-00590-0zbMath1223.20024arXivmath/0602508MaRDI QIDQ3577291

Martin Kassabov, Alexander Lubotzky, William M. Kantor, Robert M. Guralnick

Publication date: 22 July 2010

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602508

zbMATH Keywords

relationssymmetric groupspresentationsfinite simple groupsalternating groupsnumbers of generatorsgroups of Lie typeprofinite groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (22)

Presentations: from Kac-Moody groups to profinite and back ⋮ AUTOMORPHISM GROUPS OF FREE GROUPS ⋮ Describing finite groups by short first-order sentences ⋮ Presentations of finite simple groups: a computational approach. ⋮ Remarks on proficient groups. ⋮ The Dehn function of Baumslag's metabelian group. ⋮ First cohomology groups of Chevalley groups in cross characteristic. ⋮ Effective black-box constructive recognition of classical groups. ⋮ A practical model for computation with matrix groups. ⋮ Short presentations for alternating and symmetric groups ⋮ Light matrices of prime determinant ⋮ Presentations of finite simple groups: profinite and cohomological approaches. ⋮ Presentations of matrix rings ⋮ The norm of a Ree group ⋮ On presentations for unitary groups ⋮ Presentations on standard generators for classical groups ⋮ Equivariant group presentations and the second homology group of the Torelli group ⋮ PRESENTATIONS OF AFFINE KAC–MOODY GROUPS ⋮ Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory ⋮ CLASSIFYING NONEQUIVALENT PRESENTATIONS OF FINITE GROUPS - THE CASE OF DICYCLIC GROUPS ⋮ Black box exceptional groups of Lie type ⋮ Bounding cohomology for finite groups and Frobenius kernels.

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