标题： 一个广义的Goursat引理 显示英文标题

标题： A Generalized Goursat Lemma

摘要： 在本文中，通常的Goursat引理被推广，该引理描述了两个群的直积的子群，现在用于描述有限多个群的直积$A_1\times A_2 \times...\times A_n$的子群。 讨论了其他可能的推广，并给出了用于表征几种类型子群的应用。 这些应用中的大多数是直接的，而在紧致群、循环群以及Sylow$p$-子群（包括虚拟$p$-群的无限群）的情况下，出现了更深入的应用。 显示英文摘要

摘要： In this note the usual Goursat lemma, which describes subgroups of the direct product of two groups, is generalized to describing subgroups of a direct product $A_1\times A_2 \times...\times A_n$ of a finite number of groups. Other possible generalizations are discussed and applications characterizing several types of subgroups are given. Most of these applications are straightforward, while somewhat deeper applications occur in the case of profinite groups, cyclic groups, and the Sylow $p$-subgroups (including infinite groups that are virtual $p$-groups).