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} }