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OnCSQ-normal subgroups of finite groups

Yong XuXianhua Li — 2016

Open Mathematics

We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.

On supplements of subgroups of finite groups

Xianhua LiA. Ballester-Bolinches — 2006

Bollettino dell'Unione Matematica Italiana

In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.

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