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

doi:10.1016/j.jalgebra.2017.07.009

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

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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 (ε_qd−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
Pages (from-to)	241-255
Number of pages	15
Journal	Journal of Algebra
Volume	490
DOIs	https://doi.org/10.1016/j.jalgebra.2017.07.009
Publication status	Published - 15 Nov 2017

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10.1016/j.jalgebra.2017.07.009

https://arxiv.org/pdf/1602.07829.pdf

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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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AU - Verret, Gabriel

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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.

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.

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ER -

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

Abstract

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