Action of a Frobenius-like group with fixed-point free kernel
نویسندگان
چکیده
منابع مشابه
Action of a Frobenius-like group with fixed-point free kernel
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 nont...
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A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h ∈ H. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with [F ′, H] = 1. In case where CG(F ) = 1 we prove that the groups G and CG(H) have the same nilpotent length un...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2014
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt-2014-0002