A theory of semiprimitive groups

Michael Giudici, Luke Morgan

    Research output: Contribution to journalArticle

    2 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

    Fingerprint

    Permutation group
    Primitive Group
    Semiregular
    Universal Algebra
    Collapsing
    Monoids
    Normal subgroup
    Open Problems
    Quotient
    Finite Group
    Graph in graph theory
    Class

    Cite this

    Giudici, Michael ; Morgan, Luke. / A theory of semiprimitive groups. In: Journal of Algebra. 2018 ; Vol. 503. pp. 146-185.
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    A theory of semiprimitive groups. / Giudici, Michael; Morgan, Luke.

    In: Journal of Algebra, Vol. 503, 01.06.2018, p. 146-185.

    Research output: Contribution to journalArticle

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    AU - Giudici, Michael

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