Finite Transitive Permutation Groups and Bipartite Vertex-Transitive Graphs

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    Abstract

    We prove a Structure theorem for a class of finite transitive permutation groups that arises in the study of finite bipartite vertextransitive graphs. The class consists of all finite transitive permutation groups such that each non-trivial normal subgroup has at most two orbits, and at least one such subgroup is intransitive. The theorem is analogous to the O'Nan-Scott Theorem for finite primitive permutation groups, and this in turn is a refinement of the Baer Structure Theorem for finite primitive groups. An application is given for arc-transitive graphs.
    Original languageEnglish
    Pages (from-to)461-475
    JournalIllinois Journal of Mathematics
    Volume47
    Issue number1-2
    Publication statusPublished - 2003

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