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  • Author or Editor: Yangming Li x
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We use ?-quasinormal condition on minimal subgroups to Characterize the structure of a finite group through the theory of formation. We give some equivalent conditions of a nilpotent group or a saturated formation containing the nilpotent groups. Our results generalize earlier theorems of Yokoyama, Ballester-Bolinches and Pedraza Aguilera.

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Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively.

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