Abstract
Let \(\mathfrak{X}\) be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, \(\mathfrak{X}\) contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be \(\mathfrak{X}\)-permutable in G if H permutes with every member of \(\mathfrak{X}\). In this paper we characterize p-nilpotency of finite groups G; we will assume that some minimal subgroups or 2-minimal subgroups of G are \(\mathfrak{X}\)-permutable in G. Moreover, the duals of some recent results are obtained.
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Supported by the NSF of China(10571128) and the NSF of Colleges and Suzhou City Senior Talent Supporting Project.
Project supported in part by NSF of China (10571181), NSF of Guangdong Province (06023728) and ARF(GDEI).
Project supported in part by the NSF for youth of Shanxi Province (2007021004) and TianYuan Fund of Mathematics of China (10726002).
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Li, X., Li, Y. & Wang, L. \(\mathfrak{X}\)-permutable subgroups and p-nilpotency of finite groups II. Isr. J. Math. 164, 75–85 (2008). https://doi.org/10.1007/s11856-008-0021-6
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DOI: https://doi.org/10.1007/s11856-008-0021-6