Some geometries that are almost buildings

DOI10.1016/S0195-6698(81)80031-5zbMath0514.51006OpenAlexW2078043839MaRDI QIDQ1051256

William M. Kantor

Publication date: 1981

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0195-6698(81)80031-5

zbMATH Keywords

sporadic simple groupsgeneralized polygonsdiagramsBuekenhout-Tits geometries buildingsGABsgeometries that are almost buildings

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Simple groups: sporadic groups (20D08) Incidence structures embeddable into projective geometries (51A45)

Related Items (29)

Near polygons and Fischer spaces ⋮ Universal presheaves on group geometries, and modular representations ⋮ Locally finite classical Tits chamber systems of large order ⋮ On geometries of the Fischer groups ⋮ A lattice theoretical construction of a GAB of the Suzuki sporadic simple group ⋮ A root system for the Lyons group ⋮ On the universal embedding of the near-hexagon for \(U_ 4(3)\) ⋮ Some locally finite flag-transitive buildings ⋮ Some homotopy equivalences for sporadic geometries ⋮ A finite flag-transitive geometry of extended \(G_ 2\)-type ⋮ A geometric condition for incidence-matrix nullvectors ⋮ The hyperplanes of the \(U_{4}(3)\) near hexagon ⋮ Distance-transitive representations of the sporadic groups ⋮ On the linearity of lattices in affine buildings and ergodicity of the singular Cartan flow ⋮ Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2 ⋮ An algorithmic approach to fundamental groups and covers of combinatorial cell complexes ⋮ The generating rank of the \(U_{4}(3)\) near hexagon ⋮ Two new classes of hyperplanes of the dual polar space \(DH(2n-1,4)\) not arising from the Grassmann embedding ⋮ The Action of the Group, q Even, and Related Combinatorial Structures ⋮ C-groups of \(\mathrm{PSL}(2,q)\) and \(\mathrm{PGL}(2,q)\). ⋮ Triangle groups ⋮ Some projective modules determined by sporadic geometries ⋮ Chamber graphs of minimal parabolic sporadic geometries ⋮ Some sporadic geometries related to PG(3,2) ⋮ Chamber graphs of some geometries that are almost buildings ⋮ Tits geometries over gf(2) Defined by groups over gf(3) ⋮ The universal embedding for the involution geometry of \(Co_1\) ⋮ Some exceptional 2-adic buildings ⋮ Minimal parabolic geometries for the sporadic groups

Cites Work

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• Diagrams for geometries and groups
• Evidence for a new finite simple group

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