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Finite groups having nonnormal TI subgroups

Kızmaz, Muhammet Yasir
In the present paper, the structure of a finite group G having a nonnormal T.I. subgroup H which is also a Hall pi-subgroup is studied. As a generalization of a result due to Gow, we prove that H is a Frobenius complement whenever G is pi-separable. 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.