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

Abstract

Let G be a fnite group and P a subgroup of order 3. In this paper we proved some results about the soluble subgroups generated by three conjugates of P and we use these results to produce some properties of the group G.

On representations of groups of odd order

“…Let G be a finite soluble group of odd order generated by the conjugacy class of a cyclic group P of prime order. If V is a faithful irreducible G-module over a field then dim C V ðPÞ < The proof uses results on the Fitting height of a soluble group by Flavell in [4] and by Al-Roqi and Flavell in [1], [2], [3].…”

“…The properties of the soluble groups generated by four conjugates of some element have been discussed in [1] and the case of soluble groups generated by three conjugates has been discussed in [2]. Using Theorem 1.1, we derive some properties of soluble groups of odd order that are generated by two conjugates of an element of prime order.…”