Subgroups of classical groups that are transitive on subspaces

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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 classical generalised quadrangles.

Original languageEnglish
Pages (from-to)804-868
Number of pages65
JournalJournal of Algebra
Publication statusPublished - 15 Dec 2023

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