In recent years,a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group.However,about the cover-avoiding property of subgroups for non-chief factor,there is no study up to now.The purpose of this paper is to build the theory.Let A be a subgroup of a finite group G and Σ:G0≤G1≤…≤Gn some subgroup series of G.Suppose that for each pair(K,H) such that K is a maximal subgroup of H and G i 1 K < H G i for some i,either A ∩ H = A ∩ K or AH = AK.Then we say that A is Σ-embedded in G.In this paper,we study the finite groups with given systems of Σ-embedded subgroups.The basic properties of Σ-embedded subgroups are established and some new characterizations of some classes of finite groups are given and some known results are generalized.
假定 G 是一个有限的组， H 是 G 的亚群。如果， H 被说 s-quasinormally 在 G 被嵌入为划分 |H| 的各主要的 p， H 的 Sylow p 亚群也是 G 的某 s-quasinormal 亚群的 Sylow p 亚群；H 被称为 c * 如果有 G 的亚群 T， -quasinormally 在 G 嵌入以便 G = HT 和 HT s-quasinormally 在 G 被嵌入。我们调查 c 的影响 * 有限的组的结构上的 -quasinormally 嵌入的亚群。一些最近的结果被概括。
