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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 language | English |
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Pages (from-to) | 667-694 |

Number of pages | 28 |

Journal | Journal of Group Theory |

Volume | 21 |

Issue number | 4 |

Early online date | Apr 2018 |

DOIs | |

Publication status | Published - 1 Jul 2018 |

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Dive into the research topics of 'Primary cyclic matrices in irreducible matrix subalgebras'. Together they form a unique fingerprint.## Projects

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