Action of a Frobenius-like group

Güloǧlu, Ismail Ş.
Ercan, Gülin
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 is an element of 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.

Citation Formats
I. Ş. Güloǧlu and G. Ercan, “Action of a Frobenius-like group,” Journal of Algebra, vol. 402, pp. 533–543, 2014, Accessed: 00, 2020. [Online]. Available: