On the influence of fixed point free nilpotent automorphism groups
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KünyeErcan, G., Guloglu, İ. S. (2017). On the influence of fixed point free nilpotent automorphism groups. Monatshefte Fur Mathematik, 184(4), 531-538. http://dx.doi.org/10.1007/s00605-016-0970-5
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 for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the nilpotent length of by at most one. As a corollary, we also prove that for any set of primes , the upper -series of coincides with the intersections of with the upper -series of G, and the - length of G exceeds the -length of by at most one.