Finite groups having nonnormal TI subgroups


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Kizmaz M. Y.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, cilt.28, ss.905-914, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 28 Konu: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s021819671850039x
  • Dergi Adı: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Sayfa Sayıları: ss.905-914

Özet

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.