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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Li, Y., Wang, Y. & Wei, H. On p-nilpotency of finite groups with some subgroups π-quasinormally embedded. Acta Math Hung 108, 283–298 (2005). https://doi.org/10.1007/s10474-005-0225-8
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DOI: https://doi.org/10.1007/s10474-005-0225-8