Direct products of groups and regular orbits

We prove the following result. Let p be a prime, and let G be a finite p-solvable group that is a direct product of two non-cyclic subgroups of coprime order, and let V be some faithful irreducible module for G over some field in characteristic p. Then G has a regular orbit, that is, there exists so...

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Bibliographic Details
Published in:Journal of algebra 2018-01, Vol.494, p.137-141
Main Authors: Keller, Thomas Michael, Turull, Alexandre, Wolf, Thomas R.
Format: Article
Language:English
Subjects:
Finite groups
Regular orbits
Representations
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Summary:We prove the following result. Let p be a prime, and let G be a finite p-solvable group that is a direct product of two non-cyclic subgroups of coprime order, and let V be some faithful irreducible module for G over some field in characteristic p. Then G has a regular orbit, that is, there exists some v∈V such that CG(v)=1.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.10.011