Minimal 2-local geometries for the Held and Rudvalis sporadic groups

DOI10.1016/0021-8693(82)90304-0zbMath0501.20015OpenAlexW1972446252MaRDI QIDQ1172147

Stephen D. Smith, Geoffrey Mason

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90304-0

zbMATH Keywords

sporadic simple groupsirreducible modulesRudvalis groupmaximal 2-local subgroup2-local geometryHeld group

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Combinatorial structures in finite projective spaces (51E20) Ring geometry (Hjelmslev, Barbilian, etc.) (51C05)

Related Items (8)

The flag-transitive tilde and Petersen-type geometries are all known ⋮ Irreducible modules and parabolic subgroups ⋮ Finite groups ⋮ An infinite family of simply connected flag-transitive tilde geometries ⋮ A presentation and a representation of the Held group ⋮ Structure of the maximal -local geometry point-line collinearity graph ⋮ A construction of the Held simple group ⋮ Minimal parabolic geometries for the sporadic groups

Cites Work

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• Irreducible modules and parabolic subgroups
• Projectivity and relative projectivity over group rings
• Construction of the Rudvalis group of order 145,926,144,000
• A characterization of the Rudvalis simple group of order \(2^{14} \cdot 3^3 \cdot 5^3 \cdot 7 \cdot 13 \cdot 29\) by the centralizers of noncentral involutions
• The simple groups related to \(M_{24}\)
• Homology representations of finite groups of Lie type

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