Action of a Frobenius-like group with fixed-point free kernel

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2014-09-01
Ercan, Gülin
Güloğlu, İsmail Şuayip
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
G. Ercan and İ. Ş. Güloğlu, “Action of a Frobenius-like group with fixed-point free kernel,” JOURNAL OF GROUP THEORY, vol. 17, pp. 863–873, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38368.