Action of a Frobenius-likegroup
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KünyeGÜLOĞLU, İ.Ş., ERCAN, G. (2014). Action of a Frobenius-likegroup. Journal of Algebra, Volume 402, pp. 533-543. http://dx.doi.org/10.1016/j.jalgebra.2014.01.005.
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h]=F[F,h]=F for all nonidentity elements h∈Hh∈H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.