Finite groups having nonnormal TI subgroups


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Kizmaz M. Y.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, vol.28, no.5, pp.905-914, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1142/s021819671850039x
  • Title of Journal : INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Page Numbers: pp.905-914

Abstract

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.