# three subgroups lemma

> lemma in group theory: given three subgroups X, Y, Z of a group G, if [[X,Y],Z]=[[Y,Z],X]=1, then [[Z,X],Y]=1 (where brackets denote commutators)

**Wikidata**: [Q7798010](https://www.wikidata.org/wiki/Q7798010)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Three_subgroups_lemma)  
**Source**: https://4ort.xyz/entity/three-subgroups-lemma