TY - JOUR

T1 - Triple factorisations of the general linear group and their associated geometries

AU - Alavi, Hassan

AU - Bamberg, John

AU - Praeger, Cheryl

PY - 2015/3/15

Y1 - 2015/3/15

N2 - © 2014 Elsevier Inc. 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).

AB - © 2014 Elsevier Inc. 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).

U2 - 10.1016/j.laa.2014.11.018

DO - 10.1016/j.laa.2014.11.018

M3 - Article

VL - 469

SP - 169

EP - 203

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -