TITLE: How to find the derived subgroup of a given group
QUESTION [7 upvotes]: Given a group $(G, \cdot)$ is there a way to find its derived subgroup other than calculating it by hand element by element?
For instance, if a group is abelian you know that its derived subgroup is $\{1_G \}$. This is one simple example but is there a similar trick to use to make it easier to calculate $G'$?
Thanks in advance

REPLY [2 votes]: There are several characterizations of the derived subgroup. See Commutator Subgroup Characterization or https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/characterization-of-the-commutator-subgroup-of-a-group/D103777CE40256FB37E2F7B2085F2788 or https://www.tandfonline.com/doi/pdf/10.1080/00927879208824542