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On the number of Sylow subgroups in finite simple groups
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-17 , DOI: 10.1142/s0219498821501152 Zhenfeng Wu 1
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-17 , DOI: 10.1142/s0219498821501152 Zhenfeng Wu 1
Affiliation
Denote by ν p ( G ) the number of Sylow p -subgroups of G . For every subgroup H of G , it is easy to see that ν p ( H ) ≤ ν p ( G ) , but ν p ( H ) does not divide ν p ( 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 ν p ( H ) divides ν p ( 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:
关于有限单群中 Sylow 子群的个数
表示为ν p ( G ) 西洛的数量p - 亚组G . 对于每个子组H 的G ,不难看出ν p ( H ) ≤ ν p ( G ) , 但ν p ( H ) 不分ν p ( 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ν p ( H ) 划分ν p ( 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) .
更新日期:2020-07-17
中文翻译:
关于有限单群中 Sylow 子群的个数
表示为