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Finite Groups with Weakly s-Permutably Embedded and Weakly s-Supplemented Subgroups

100%

Li C.

tom 59

nr 1

41-52

Suppose G is a finite group and H is a subgroup of G. H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup $H_{se}$ of G contained in H such that G = HT and $H ∩ T ≤ H_{se}$; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and $H ∩ T ≤ H_{sG}$, where $H_{sG}$ is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We investigate the influence of the existence of s-permutably embedded and weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized.

On E-S-supplemented subgroups of finite groups

51%

Li C. , Zhang X. , Yi X.

Colloquium Mathematicum

2013

tom 131

nr 1

41-51

The major aim of the present paper is to strengthen a nice result of Shemetkov and Skiba which gives some conditions under which every non-Frattini G-chief factor of a normal subgroup E of a finite group G is cyclic. As applications, some recent known results are generalized and unified.