Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...

In this paper, we prove the p-nilpotency of a finite group with assumption that some subgroups of Sylow subgroup are weakly s-semipermutable subgroups in the normalizer of Sylow subgroups. Our results unify and generalize some earlier results. Mathematics Subject Classification: 20D10, 20D15

In this paper, we investigate the influence of Ssemipermutable and weakly S-supplemented subgroups on the pnilpotency of finite groups. Some recent results are generalized. Keywords—S-semipermutable, weakly S-supplemented, pnilpotent.

In this note, we obtain some criteria for p-supersolvablity of a finite group and extend some known results concerning weakly S-semipermutable subgroups. Mathematics Subject Classification (2010). 20D10.

Let $G$ be a finite group. A subgroup $H$ is called $S$-semipermutable in if $HG_p$ = $G_pH$ for any $G_p\in Syl_p(G)$ with $(|H|, p) 1$, where $p$ prime number divisible $|G|$. Furthermore, said to $NH$-embedded there exists normal $T$ of such that $HT$ Hall and $H \cap T \leq H_{\overline{s}G}$, $H_{\overline{s}G}$ the largest contained $H$, $SS$-quasinormal provided supplement $B$ permutes e...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...