On the influence of fixed point free nilpotent automorphism groups
MetadataShow full item record
CitationErcan, 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.