Finite groups having nonnormal T.I. subgroups

Abstract

In the present paper, the structure of a finite group G having a nonnormal T.I. subgroup H which is also a Hall πsubgroup is studied. As a generalization of a result due to Gow, we prove that H is a Frobenius complement whenever G is πseparable. This is achieved by obtaining the fact that Hall T.I. subgroups are conjugate in a finite group. We also prove two theorems about normal complements one of which generalizes a classical result of Frobenius.