Alternating Groups Acting on Finite Linear Spaces

A.R. Camina, P.M. Neumann, Cheryl Praeger

    Research output: Contribution to journalArticlepeer-review

    37 Citations (Scopus)

    Abstract

    This is a contribution to the study of line-transitive groups of automorphisms of finite linear spaces. Groups which are almost simple are of particular importance. In this paper almost simple line-transitive groups whose socle is an alternating group are classified. It is proved that the only alternating groups to occur are those of degrees 7 and 8, and that only one linear space occurs, namely a well-known space with 15 points and 35 lines. Although much of the proof exploits special properties of alternating groups, some general theory of groups acting line-transitively on finite linear spaces is developed.
    Original languageEnglish
    Pages (from-to)29-53
    JournalProceedings of the London Mathematical Society
    Volume87
    Issue number1
    DOIs
    Publication statusPublished - 2003

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