In this paper, we introduce the concept of weakly s-semipermutable subgroups. Let G be a finite group. Using the condition that the minimal subgroups or subgroups of order p2 of a given Sylow p-subgroup of G are weakly s-semipermutable in G, we give a criterion for p-nilpotency of G and get some results about formation.

https://rd.springer.com/content/pdf/10.1007%2Fs11464-010-0081-x.pdf

Weakly s -semipermutable subgroups of finite groups

Suppose that G is a finite group and H is a subgroup of G. We say that H is s-semipermutable in G if H Gp = GpH for any Sylow p-subgroup Gp of G with (p, |H|) = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.

On s-semipermutable subgroups of finite groups

LetH be a subgroup of a finite groupG. We say that: (1)H is -quasinormal inG if H permutes with every Sylow subgroupQ ofG such that.jHj;jQj/D1 and.jHj;jQ G j/⁄1; (2)H is -supplemented inG ifG has a subgroupT ofG such thatGDHT andH\T HG , whereHG is the subgroup generated by all those subgroups ofH which are -quasinormal in G. We investigate the influence of -supplemented subgroups on the structure of finite groups. Some recent known results are generalized and unified. 2010 Mathematics Subject Classification: 20D10; 20D20

/pdf/on-supplemented-subgroups-of-finite-groups-18yvg69juj.pdf

On -supplemented subgroups of finite groups

In this paper, we prove the following theorem: Let p be a prime number, P aS ylowp- subgroup of a group G and π = π(G) \{ p}. If P is seminormal in G, then the following statements hold :1 )G is a p-soluble group and P ≤ Op(G); 2) lp(G) ≤ 2 and lπ(G) ≤ 2; 3) if a π-Hall subgroup of G is q-supersoluble for some q ∈ π ,t henG is q-supersoluble. Keywords finite groups, seminormal subgroups, Sylow subgroups, p-soluble groups, p-supersoluble groups

Finite groups with seminormal Sylow subgroups

A subgroup H of a finite group G is said to be nearly s-embedded in G if G has an s-permutable subgroup T and an s-semipermutable subgroup HssG contained in H such that HsG=HT and H∩T≤HssG, where H...

Nearly s-embedded subgroups and the p-nilpotency of finite groups

A subgroup H of a finite group G is called s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with(p,|H|)=1. In this paper, the influence of s-semipermutable subgroups on the structure of finite groups is investigated.

Chang-Wen Li

Papers

The Influence of s-semipermutable Subgroups on the Structure of Finite Groups