A theory of semiprimitive groups

Michael Giudici, Luke Morgan

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids and the graph-restrictive problem for permutation groups. Here we develop a theory of semiprimitive groups which encompasses their structure, their quotient actions and a method by which all finite semiprimitive groups are constructed. We also extend some results from the theory of primitive groups to semiprimitive groups, and conclude with open problems of a similar nature.

    Original languageEnglish
    Pages (from-to)146-185
    Number of pages40
    JournalJournal of Algebra
    Volume503
    DOIs
    Publication statusPublished - 1 Jun 2018

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