Primary cyclic matrices in irreducible matrix subalgebras

Brian P. Corr, Cheryl E. Praeger

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    Abstract

    Primary cyclic matrices were used (but not named) by Holt and Rees in their version of Parkers MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices X with at least one cyclic component in the primary decomposition of the underlying vector space as an X-module. Let M.c; qb/ be an irreducible subalgebra of M.n; q/, where n D bc > c. We prove a generalisation of the KungStong cycle index theorem, and use it to obtain a lower bound for the proportion of primary cyclic matrices in M.c; qb/. This extends work of Glasby and the second author on the case b D 1.

    Original languageEnglish
    Pages (from-to)667-694
    Number of pages28
    JournalJournal of Group Theory
    Volume21
    Issue number4
    Early online dateApr 2018
    DOIs
    Publication statusPublished - 1 Jul 2018

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