Finite groups having nonnormal TI subgroups
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, vol.28, no.5, pp.905-914, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 28 Issue: 5
- Publication Date: 2018
- Doi Number: 10.1142/s021819671850039x
- Journal Name: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.905-914
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
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.