### 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

*Journal of Algebra*,

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

}

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

**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.

Research output: Contribution to journal › Article

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

Y1 - 2017/11/15

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.

AB - 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.

KW - Completely reducible grouops

KW - Composition factors

UR - http://www.scopus.com/inward/record.url?scp=85026455426&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.07.009

DO - 10.1016/j.jalgebra.2017.07.009

M3 - Article

VL - 490

SP - 241

EP - 255

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -