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A note on number of Sylow subgroups of finite groups. (Chinese. English summary) Zbl 1224.20020

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 \(n\geqslant 1\).

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MSC:

20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D60 Arithmetic and combinatorial problems involving abstract finite groups
20E28 Maximal subgroups

Citations:

Zbl 0832.20042
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