On the Fitting height of a soluble group that is generated by a conjugacy class of 3-elements

Abstract

Let G be a finite soluble group that is generated by a conjugacy class consisting of elements of order 3. We show that there exist four conjugates of an element of order 3 that generate a subgroup with the same Fitting height as G. We use this result to find a soluble analogue of the Baer–Suzuki theorem in the case prime 3.