Action of a Frobenius-like group with fixed-point free kernel
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KünyeERCAN, G., GÜLOĞLU, İ.Ş. (2014). Action of a frobenius-like group with fixed-point free kernel. Journal of Group Theory, 17 (5) pp. 863-873. http://dx.doi.org/10.1515/jgt-2014-0002.
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 for all nonidentity elements h ∈ 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.
KaynakJournal of Group Theory