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A note on number of Sylow subgroups of finite groups. (Chinese. English summary) Zbl 1224.20020
Summary: The result of {\it 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 $n\geqslant 1$.
MSC:
20D20Sylow subgroups of finite groups, Sylow properties, $\pi$-groups, $\pi$-structure
20D60Arithmetic and combinatorial problems on finite groups
20E28Maximal subgroups of groups
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