理论数学

Vol.6 No.3 (May 2016)

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。

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

 

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