π-可分群的Hall π-子群的个数
The Number of Hall π-Subgroups of a π-Separable Group
DOI: 10.12677/PM.2016.63024, PDF,    国家自然科学基金支持
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: 设G是有限π-可分群，H是G的任意Hall π-子群，K是G的子群。Alexandre Turull利用Hall π-子群的计算公式得到G的Hall π-子群H的个数可以被其子群K的Hall 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. π-可分群的Hall π-子群的个数[J]. 理论数学, 2016, 6(3): 162-165. https://dx.doi.org/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 [Google Scholar] [CrossRef] 
[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 [Google Scholar] [CrossRef] 
[3] Isaacs, I.M. (2008) Finite Group Theory. American Ma-thematical Society, Providence. http://dx.doi.org/10.1090/gsm/092 [Google Scholar] [CrossRef] 
[4] 徐明曜. 有限群初步[M]. 北京: 科学出版社, 2013.

为你推荐