有限π-可分群的Hall子群的数量(英文)

Number of Hall subgroups of finite π-separable groups

设K是有限π-可分群G的子群,则vπ(K)整除vπ(G),其中vπ(G)表示G的Hallπ-子群的数量.这个结果给出了由Navarro最近得到的一个定理的推广,并应用于确定某些有限群的π'-闭性质.

If K is a subgroup of a finite π-separable group G,denote by vπ（G） the number of Hall π-subgroups of G,then vπ（K） divides vπ（G）.This result extends a theorem recently obtained by Navarro and is applied to determine the π′-closed property of some finite groups.