On Permutable Subgroups of n-ary Groups

On W -S-permutable Subgroups of Finite Groups∗

A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

groups with all subgroups permutable or soluble

in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

On N-high Subgroups of Abelian Groups

On Ss-quasinormal and Weakly S-permutable Subgroups of Finite Groups

A subgroup H of a group G is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is called weakly s-permutable in G if there is a subnormal subgroup T of G such that G = 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. We fix in every non-cyclic Sylow subgr...