If is a finitely generated profinite group then the verbal subgroup is open. In a -generator finite group every product of th powers is a product of th powers.
Cite this article
Nikolay Nikolov, Dan Segal, Powers in finite groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 501–507DOI 10.4171/GGD/136