A Generalized Goursat Lemma
Abstract
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 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 -subgroups (including infinite groups that are virtual -groups).
Cite
@article{arxiv.1109.0024,
title = {A Generalized Goursat Lemma},
author = {Kristine Bauer and Debasis Sen and Peter Zvengrowski},
journal= {arXiv preprint arXiv:1109.0024},
year = {2015}
}
Comments
22 pages. This version is substantially changed from previous versions. We have retained the proof of Theorem 2.3, but have included attribution of this result to [Sch94]. We have substantially expanded applications to include pro-finite groups and Sylow $p$-subgroups (including infinite groups that are virtual $p$-groups), among others