On p-nilpotency of finite groups with some subgroups π-quasinormally embedded

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.

Authors and Affiliations

1. Department of Mathematics, Guangdong Institute of Education, Guangzhou, 510310, P.R. China

   Yangming Li

2. Department of Mathematics, Zhongshan University, Guangzhou, 510275, P.R. China

   Yanming Wang

3. Department of Mathematics, Guangxi Teacher’s College, Nanning, 530001, P.R. China

   Huaquan Wei

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