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

Information Systems

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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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title = "The number of composition factors of order p in completely reducible groups of characteristic p",

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 - 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 - https://www.scopus.com/pages/publications/85026455426

U2 - 10.1016/j.jalgebra.2017.07.009

DO - 10.1016/j.jalgebra.2017.07.009

M3 - Article

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SN - 0021-8693

VL - 490

SP - 241

EP - 255

JO - Journal of Algebra

JF - Journal of Algebra

ER -

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

Abstract

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