Subgroups of Classical Groups that are Transitive on Subspaces

2020/12/14 by Giudici, Michael, Glasby, S. P., Praeger, Cheryl E. · 1 citation
#05B25 #20B10 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #primary 20G40 #secondary 57S17

paper · doi:10.48550/arxiv.2012.07213

Abstract

For each finite classical group G, we classify the subgroups of G which act transitively on a G-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the classification of the maximal factorisations of almost simple groups. As a first application of these results we classify all point-transitive subgroups of automorphisms of finite thick generalised quadrangles.

Cited by

• Large maximal subgroups of almost simple classical groups

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