Overgroups of Cyclic Sylow Subgroups of Linear Groups

John Bamberg, Tim Penttila

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    We use a theorem of Guralnick, Penttila, Praeger, and Saxl to classify the subgroups of the general linear group (of a finite dimensional vector space over a finite field) which are overgroups of a cyclic Sylow subgroup. In particular, our results provide the starting point for the classification of transitive m-systems; which include the transitive ovoids and spreads of finite polar spaces. We also use our results to prove a conjecture of Cameron and Liebler on irreducible collineation groups having equally many orbits on points and on lines.
    Original languageEnglish
    Pages (from-to)2503-2543
    JournalCommunications in Algebra
    Issue number7
    Publication statusPublished - 2008

    Cite this