π-可分群的Hall π-子群的个数

The Number of Hall π-Subgroups of a π-Separable Group

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.