Remarks on proficient groups.

DOI10.1016/j.jalgebra.2009.05.018zbMath1239.20037arXiv0905.0256OpenAlexW2964029433WikidataQ101542339 ScholiaQ101542339MaRDI QIDQ2431539

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

Publication date: 15 April 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0256

zbMATH Keywords

symmetric groupsfinite simple groupsperfect groupsalternating groupsnumbers of generatorscohomology of groupsgroups of Lie typeSchur multipliersefficient presentationsfinite quasisimple groupspresentations of finite groupsfinite perfect groupsproficient presentationsprofinite presentations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Cohomology of groups (20J06) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06) Limits, profinite groups (20E18) Central extensions and Schur multipliers (19C09)

Related Items (1)

Presentations of finite simple groups: a computational approach.

Uses Software

• Magma

Cites Work

• Presentations of finite simple groups: a computational approach.
• Some applications of the first cohomology group
• On the cohomology of alternating and symmetric groups and decomposition of relation modules
• Generation of finite almost simple groups by conjugates.
• Closing the relation gap by direct product stabilization
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• Minimal resolutions for finite groups
• Exponentials in differentially algebraic extension fields
• FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS
• Presentations of finite simple groups: A quantitative approach
• Deficiency zero presentations for certain perfect groups
• Efficient Presentations of the Groups Psl (2, p ) × PSL (2, p ), p Prime
• The efficiency of simple groups of order < 10⁵
• On second degree cohomology of symmetric and alternating groups
• Decomposition of the Relation Modules of a Finite Group
• A Deficiency Zero Presentation for SL (2, p )
• The efficiency of PSL(2, p)³ and other direct products of groups
• Proficient presentations and direct products of finite groups
• Nice Efficient Presentions for all Small Simple Groups and their Covers
• On the Efficiency of the Simple Groups of Order Less Than a Million and Their Covers
• Presentations of the Groups SL(2,m) And PSL(2,m)
• Pro-finite presentations
• Embeddings into \(k\)-efficient groups.
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