Let G be a finite group. How minimal subgroups can be embedded in G is a question of particular interest in studying the structure of G. A subgroup H of G is called s-permutable in G if HP = PH for all Sylow subgroups P of G. A subgroup H of G is called n-embedded in G if there exists a normal subgroup T of G such that HG = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. In this paper, we investigate the structure of the finite group G with n-embedded subgroups.

中文翻译：

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具有 n 个嵌入子群的有限群

让G是一个有限群。最小子群如何嵌入G是研究结构的一个特别感兴趣的问题G. 一个子群H的G叫做s- 可在G如果H磷 = 磷H对于所有 Sylow 子群磷的G. 一个子群H的G叫做n-嵌入G如果存在正规子群吨的G这样HG = H吨和H ∩ 吨 ≤ HsG， 在哪里HsG是的子群H由所有这些子组生成H哪个是s- 可在G. 在本文中，我们研究了有限群的结构G和n- 嵌入式子组。