Finite groups having nonnormal TI subgroups

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2018-08-01

Author

Kızmaz, Muhammet Yasir

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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.

Subject Keywords

Normal complement, Double Frobenius group, TI subgroup, Frobenius group

URI

https://hdl.handle.net/11511/51177

Journal

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

DOI

https://doi.org/10.1142/s021819671850039x

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Department of Mathematics, Article

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Citation Formats

M. Y. Kızmaz, “Finite groups having nonnormal TI subgroups,” INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, pp. 905–914, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51177.