Shen, Rulin; Shi, Jiangtao; Shao, Changguo; Shi, Wujie A note on number of Sylow subgroups of finite groups. (Chinese. English summary) Zbl 1224.20020 J. Shanghai Univ., Nat. Sci. 16, No. 6, 639-642 (2010). Summary: The result of J.-P. Zhang [J. Algebra 176, No. 1, 111-123 (1995; Zbl 0832.20042)] on the Sylow number of finite groups is generalized. We prove that the number of Sylow \(r\)-subgroups is \(2p^n\) if and only if \(2p^n=1+r^{2m}\), where \(p\) is odd prime and \(n\geqslant 1\). MathOverflow Questions: Reference request MSC: 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20E28 Maximal subgroups Keywords:finite groups; finite simple groups; maximal subgroups; Sylow numbers; numbers of Sylow subgroups Citations:Zbl 0832.20042 PDFBibTeX XMLCite \textit{R. Shen} et al., J. Shanghai Univ., Nat. Sci. 16, No. 6, 639--642 (2010; Zbl 1224.20020) Full Text: DOI