Finite groups having nonnormal TI subgroups
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, cilt.28, sa.5, ss.905-914, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 28 Sayı: 5
- Basım Tarihi: 2018
- Doi Numarası: 10.1142/s021819671850039x
- Dergi Adı: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.905-914
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
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.