Good action of a nilpotent group with regular orbits

Abstract

Suppose that A is a finite nilpotent group of odd order having a good action, in the sense of [1], on the group G of odd order. Under some additional assumptions we prove that the Fitting height of G is bounded above by the sum of the numbers of primes dividing vertical bar A vertical bar and vertical bar C-G(A)vertical bar counted with multiplicities.