﻿ π-可分群的Hall π-子群的个数

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

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.

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http://dx.doi.org/10.1090/S0002-9939-04-07412-X

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