Triple factorisations of the general linear group and their associated geometries

2014/05/20 by Seyed Hassan Alavi, Alavi, Seyed Hassan, John Bamberg +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR

paper · pdf · doi:10.48550/arxiv.1405.5276

openalex publication_date 2014/05/20 · arxiv created 2014/05/21 · arxiv updated 2014/05/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Triple factorisations of finite groups G of the form G=PQP are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation G=PQP corresponds to a G-flag transitive point/line geometry such that `each pair of points is incident with at least one line'. We call such a geometry collinearly complete, and duality (interchanging the roles of points and lines) gives rise to the notion of concurrently complete geometries. In this paper, we study triple factorisations of the general linear group GL(V) as PQP where the subgroups P and Q either fix a subspace or fix a decomposition of V as V₁⊕ V₂ with dim(V₁)=dim(V₂).

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