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arXiv · 1801.09206

Finite Groups Having Nonnormal T.I. Subgroups

M. Yasir Kızmaz
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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.

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M. Yasir Kızmaz. 2018-01-28. Finite Groups Having Nonnormal T.I. Subgroups. https://arxiv.org/abs/1801.09206

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