Frobenius groups of automorphisms with almost fixed point free kernel


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Ercan G. , Güloğlu İ. Ş.

JOURNAL OF ALGEBRA, cilt.521, ss.384-389, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1. (C) 2018 Elsevier Inc. All rights reserved.