On the influence of fixed point free nilpotent automorphism groups


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Ercan G. , Güloğlu İ. Ş.

MONATSHEFTE FUR MATHEMATIK, cilt.184, ss.531-538, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 184
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00605-016-0970-5
  • Dergi Adı: MONATSHEFTE FUR MATHEMATIK
  • Sayfa Sayıları: ss.531-538

Özet

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.