In this note the usual Goursat lemma, which describes subgroups ofthe direct product of two groups, is generalized to describing subgroupsof a direct product \ $A_1\times A_2 \times \cdots \times A_n$ \ of afinite number of groups. Other possible generalizations are discussed and applications characterizing several types of subgroups are given. Mostof these applications are straightforward, while somewhat deeper applicationsoccur in the case of profinite groups, cyclic groups, and the Sylow $p$- subgroups (includinginfinite groups that are virtual $p$-groups).
@article{374,
title = {A generalized Goursat lemma},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v64i0.374},
language = {EN},
url = {http://dml.mathdoc.fr/item/374}
}
Bauer, Kristine; Sen, Debasis; Zvengrowski, Peter. A generalized Goursat lemma. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v64i0.374. http://gdmltest.u-ga.fr/item/374/