Presentations of finite simple groups: profinite and cohomological approaches.

DOI10.4171/GGD/22zbMath1135.20024arXiv0711.2817OpenAlexW2963331108MaRDI QIDQ2469769

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

Publication date: 7 February 2008

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2817

zbMATH Keywords

relationspresentationsfinite simple groupssecond cohomology groupsnumbers of generatorscohomology of groupsfinite quasisimple groupsprofinite presentations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Modular representations and characters (20C20) Cohomology of groups (20J06) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite simple groups and their classification (20D05)

Related Items (24)

Algorithms for Group Isomorphism via Group Extensions and Cohomology ⋮ Efficient finite groups arising in the study of relative asphericity ⋮ Presentations: from Kac-Moody groups to profinite and back ⋮ The free group on \(n\) generators modulo \(n + u\) random relations as \(n\) goes to infinity ⋮ Sectional rank and cohomology ⋮ Presentations of finite simple groups: a computational approach. ⋮ Bounding Ext for modules for algebraic groups, finite groups and quantum groups. ⋮ Unbounding Ext. ⋮ On intermediate subfactors of Goodman-de la Harpe-Jones subfactors ⋮ Counting irreducible modules for profinite groups ⋮ Remarks on proficient groups. ⋮ On a problem about tensor products of subfactors ⋮ First cohomology groups of Chevalley groups in cross characteristic. ⋮ On a subfactor generalization of Wall's conjecture ⋮ On the orders of the non-Frattini elements of a finite group ⋮ On the cohomology of \(p\)-solvable groups ⋮ Probabilistic finiteness properties for profinite groups ⋮ Presentations of finite simple groups: A quantitative approach ⋮ Cohomological growth rates and Kazhdan-Lusztig polynomials. ⋮ The Chebotarev invariant of a finite group: A conjecture of Kowalski and Zywina ⋮ PRESENTATIONS OF AFFINE KAC–MOODY GROUPS ⋮ Cohomology of \(\mathrm{PSL}_2(q)\) ⋮ Bounding the Dimensions of Rational Cohomology Groups ⋮ Bounding cohomology for finite groups and Frobenius kernels.

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