On the influence of fixed point free nilpotent automorphism groups

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2017-12-01
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.
MONATSHEFTE FUR MATHEMATIK

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Citation Formats
G. Ercan, “On the influence of fixed point free nilpotent automorphism groups,” MONATSHEFTE FUR MATHEMATIK, pp. 531–538, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44093.