Action of a Frobenius-like group with fixed-point free kernel
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چکیده
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that ŒF; h D F for all nonidentity elements h 2 H . We prove that any irreducible nontrivial FH -module for a Frobeniuslike 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.
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تاریخ انتشار 2014