Denote by νp(G) the number of Sylow p-subgroups of G. For every subgroup H of G, it is easy to see that νp(H) ≤ νp(G), but νp(H) does not divide νp(G) in general. Following [W. Guo and E. P. Vdovin, Number of Sylow subgroups in finite groups, J. Group Theory 21(4) (2018) 695–712], we say that a group G satisfies DivSyl(p) if νp(H) divides νp(G) for every subgroup H of G. In this paper, we show that “almost for every” finite simple group S, there exists a prime p such that S does not satisfy DivSyl(p).

中文翻译：

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关于有限单群中 Sylow 子群的个数

表示为νp(G)西洛的数量p- 亚组G. 对于每个子组H的G，不难看出νp(H) ≤ νp(G)， 但νp(H)不分νp(G)一般来说。继 [W. Guo 和 EP Vdovin，有限群中的 Sylow 子群数，J. 群论 21(4) (2018) 695–712]，我们说一组G满足DivSyl(p)如果νp(H)划分νp(G)对于每个子组H的G. 在本文中，我们证明了“几乎对每个”有限单群小号, 存在一个素数p这样小号不满足DivSyl(p).