Abstract

Suppose that a finite group G admits a Frobenius group of automorphisms FH with kernel F and complement H such that F acts without nontrivial fixed points (that is, such that C G(F)=1). It is proved that the Fitting height of G is equal to the Fitting height of the fixed-point subgroup C G(H) and the Fitting series of C G(H) coincides with the intersections of C G(H) with the Fitting series of G. As a corollary, it is also proved that for any set of primes � the �-length of G is equal to the �-length of C G(H). © 2012 Elsevier Inc.