Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subg...Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.展开更多
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditional...A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.展开更多
A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable group...A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.展开更多
文摘Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
基金The Scientific Research Foundation of Sichuan Provincial Education Department of China(No.08zb082)
文摘A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.
文摘A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.
