Let G be a finite group. A subgroup H of G is called an \documentclass{aastex}
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$$\mathcal{H}$$
\end{document}-subgroup in G if NG(H) ∩ Hg ≤ H for all g ∈ G. A subgroup H of G is called a weakly \documentclass{aastex}
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$$\mathcal{H}$$
\end{document}-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an \documentclass{aastex}
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$$\mathcal{H}$$
\end{document}-subgroup in G. In this article, we investigate the structure of a group G in which every subgroup with order pm of a Sylow p-subgroup P of G is a weakly \documentclass{aastex}
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$$\mathcal{H}$$
\end{document}-subgroup in G, where m is a fixed positive integer. Our results improve and extend the main results of Skiba [13], Jaraden and Skiba [11], Guo and Wei [8], Tong-Veit [15] and Li et al. [12].
Influence of weakly H-subgroups of minimal subgroups on the structure of finite groups
