Volume 49, Issue 1
On Fτ-s-supplemented Subgroups of Finite Groups

J. Math. Study, 49 (2016), pp. 50-56.

Published online: 2016-03

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• Abstract

Let \mathfrak{F} be a non-empty formation of groups, τ a subgroup functor and H a p-subgroup of a finite group G. Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G$. We say that H is $\mathfrak{F}_τ-$ s-supplemented in G if for some subgroup $\overline{T}$ and some τ-subgroup $\overline{S}$of $\overline{G}$ contained in $\overline{H}, \overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z\mathfrak{F}(\overline{G}$). In this paper, we investigate the influence of $\mathfrak{F}_τ-$ s-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.

• Keywords

Subnormal subgroup subgroup functor soluble group

20D10 20D15 20D20

maoym@mail.ustc.edu.cn (Yuemei Mao)

mxj790808@163.com (Xiaojian Ma)

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@Article{JMS-49-50, author = {Mao , Yuemei and Ma , Xiaojian }, title = {On Fτ-s-supplemented Subgroups of Finite Groups}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {1}, pages = {50--56}, abstract = {

Let \mathfrak{F} be a non-empty formation of groups, τ a subgroup functor and H a p-subgroup of a finite group G. Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G$. We say that H is $\mathfrak{F}_τ-$ s-supplemented in G if for some subgroup $\overline{T}$ and some τ-subgroup $\overline{S}$of $\overline{G}$ contained in $\overline{H}, \overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z\mathfrak{F}(\overline{G}$). In this paper, we investigate the influence of $\mathfrak{F}_τ-$ s-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n1.16.06}, url = {http://global-sci.org/intro/article_detail/jms/988.html} }
TY - JOUR T1 - On Fτ-s-supplemented Subgroups of Finite Groups AU - Mao , Yuemei AU - Ma , Xiaojian JO - Journal of Mathematical Study VL - 1 SP - 50 EP - 56 PY - 2016 DA - 2016/03 SN - 49 DO - http://dor.org/10.4208/jms.v49n1.16.06 UR - https://global-sci.org/intro/article_detail/jms/988.html KW - Subnormal subgroup KW - subgroup functor KW - soluble group AB -

Let \mathfrak{F} be a non-empty formation of groups, τ a subgroup functor and H a p-subgroup of a finite group G. Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G$. We say that H is $\mathfrak{F}_τ-$ s-supplemented in G if for some subgroup $\overline{T}$ and some τ-subgroup $\overline{S}$of $\overline{G}$ contained in $\overline{H}, \overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z\mathfrak{F}(\overline{G}$). In this paper, we investigate the influence of $\mathfrak{F}_τ-$ s-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.

Yuemei Mao & Xiaojian Ma. (2019). On Fτ-s-supplemented Subgroups of Finite Groups. Journal of Mathematical Study. 49 (1). 50-56. doi:10.4208/jms.v49n1.16.06
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