### 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 (ε_{q}d−1)/(p−1), where ε_{q} is a function of q satisfying 1⩽ε_{q}⩽3/2. For every q, we give examples showing this bound is sharp infinitely often.

Original language | English |
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Pages (from-to) | 241-255 |

Number of pages | 15 |

Journal | Journal of Algebra |

Volume | 490 |

DOIs | |

Publication status | Published - 15 Nov 2017 |

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## Cite this

Giudici, M., Glasby, S. P., Li, C. H., & Verret, G. (2017). The number of composition factors of order p in completely reducible groups of characteristic p.

*Journal of Algebra*,*490*, 241-255. https://doi.org/10.1016/j.jalgebra.2017.07.009