The number of composition factors of order p in completely reducible groups of characteristic p

Michael Giudici, S. P. Glasby, Cai Heng Li, Gabriel Verret

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    Let q be a power of a prime p and let G be a completely reducible subgroup of GL(d,q). We prove that the number of composition factors of G that have prime order p is at most (εqd−1)/(p−1), where εq is a function of q satisfying 1⩽εq⩽3/2. For every q, we give examples showing this bound is sharp infinitely often.

    Original languageEnglish
    Pages (from-to)241-255
    Number of pages15
    JournalJournal of Algebra
    Volume490
    DOIs
    Publication statusPublished - 15 Nov 2017

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    Giudici, Michael ; Glasby, S. P. ; Li, Cai Heng ; Verret, Gabriel. / The number of composition factors of order p in completely reducible groups of characteristic p. In: Journal of Algebra. 2017 ; Vol. 490. pp. 241-255.
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    abstract = "Let q be a power of a prime p and let G be a completely reducible subgroup of GL(d,q). We prove that the number of composition factors of G that have prime order p is at most (εqd−1)/(p−1), where εq is a function of q satisfying 1⩽εq⩽3/2. For every q, we give examples showing this bound is sharp infinitely often.",
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    The number of composition factors of order p in completely reducible groups of characteristic p. / Giudici, Michael; Glasby, S. P.; Li, Cai Heng; Verret, Gabriel.

    In: Journal of Algebra, Vol. 490, 15.11.2017, p. 241-255.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - The number of composition factors of order p in completely reducible groups of characteristic p

    AU - Giudici, Michael

    AU - Glasby, S. P.

    AU - Li, Cai Heng

    AU - Verret, Gabriel

    PY - 2017/11/15

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    N2 - Let q be a power of a prime p and let G be a completely reducible subgroup of GL(d,q). We prove that the number of composition factors of G that have prime order p is at most (εqd−1)/(p−1), where εq is a function of q satisfying 1⩽εq⩽3/2. For every q, we give examples showing this bound is sharp infinitely often.

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    KW - Composition factors

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