Powers in finite groups

Abstract

In this note we prove that if $G$ is a finitely generated profinite group then the verbal subgroup $G^q$ is open. Equivalently in a $d$-generator finite group every product of $q$th powers is a product of $f(d,q)$ $q$th powers.

7 pages

Cited by in corpus (3)

• Generators and commutators in finite groups; abstract quotients of compact groups
• Word equations in simple groups and polynomial equations in simple algebras
• Bounded Engel elements in residually finite groups