FINITE GROUPS WITH ∨ 𝑠𝑝-EMBEDDED SUBGROUPS
Throughout the paper, all groups are finite and G always denotes a finite group. We say that a subgroup of G is ∨ 𝑠𝑝-embedded in G if = ⟨𝐿, 𝑇⟩, where L is 𝔘-normal and T is S-permutable subgroups of G. We also provide to consider the following new property of embedded subgroups of finite groups: H is weakly ∨ 𝑠𝑝-embedded in G if G has a subnormal subgroup K such that = 𝐻𝐾, ≤ и ∣ ∩ 𝐾: ∣ is a p'-number, where denotes the subgroup of H generated by all those subgroups of H which are ∨ 𝑠𝑝-embedded in G.The purpose of the research is to investigate the relationship between the weakly ∨ 𝑠𝑝-embedding of maximal subgroups and the solvability of a group.Material and methods. Methods of the study of the finite group theory are used.Findings and their discussion. Let be a group and ∈ 𝜋(𝐺). If every element of 𝔍p(G) is weakly ∨ 𝑠𝑝-embedded in then 𝐺is p-soluble.Conclusion. The new property of embedded subgroups of finite groups was found.