π-可分群的Hall π-子群的个数
The Number of Hall π-Subgroups of a π-Separable Group

作者: 方树珍 * , 李 欣 , 周 芳 :太原师范学院数学系,山西 晋中;

关键词: Hall π-子群有限π-可分群整除Hall π-Subgroup π-Separable Finite Group Divisibility

摘要:
G是有限π-可分群,HG的任意Hall π-子群,KG的子群。Alexandre Turull利用Hall π-子群的计算公式得到GHall π-子群H的个数可以被其子群KHall π-子群的个数整除这一关系。本文用初等方法证明了该结论。

Abstract: Let G be a π-separable finite group, K and H respectively a subgroup and any Hall πsubgroup of G. Alexandre Turull gets the divisibility relation between the number of Hall π-subgroups of G and that of K by using the calculation formula about the number of Hall π-subgroup. It is obtained the form of certificate by using the elementary method.

文章引用: 方树珍 , 李 欣 , 周 芳 (2016) π-可分群的Hall π-子群的个数。 理论数学, 6, 162-165. doi: 10.12677/PM.2016.63024

参考文献

[1] Turull, A. (2004) The Number of Hall π-Subgroups of a π-Separable Group. Proceedings of the American Mathematical Society, 132, 2563-2565.
http://dx.doi.org/10.1090/S0002-9939-04-07412-X

[2] Navarro, G. (2003) Number of Sylow Subgroups in p-Solvable Groups. Proceedings of the American Mathematical Society, 131, 3019-3020.
http://dx.doi.org/10.1090/S0002-9939-03-06884-9

[3] Isaacs, I.M. (2008) Finite Group Theory. American Ma-thematical Society, Providence.
http://dx.doi.org/10.1090/gsm/092

[4] 徐明曜. 有限群初步[M]. 北京: 科学出版社, 2013.

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