On the influence of fixed point free nilpotent automorphism groups


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Ercan G., Güloğlu İ. Ş.

MONATSHEFTE FUR MATHEMATIK, vol.184, pp.531-538, 2017 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 184
  • Publication Date: 2017
  • Doi Number: 10.1007/s00605-016-0970-5
  • Journal Name: MONATSHEFTE FUR MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.531-538

Abstract

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.