On the orders of composition factors in completely reducible groups

We obtain an asymptotic upper bound for the product of the p-parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime p. This enables us to give a new bound for the diameter of a nondiagonal...

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Bibliographic Details
Published inJournal of algebra Vol. 645; pp. 183 - 196
Main Authors Maróti, Attila, Skresanov, Saveliy V.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2024
Subjects
Completely reducible
Composition factor
Orbital graph
Simple group of Lie type
20C33
Orbital graph
Simple group of Lie type
Composition factor
20E34
Completely reducible
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Summary:We obtain an asymptotic upper bound for the product of the p-parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime p. This enables us to give a new bound for the diameter of a nondiagonal orbital graph of an affine primitive permutation group.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2024.02.001