Groups, Geometry, and Dynamics

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Volume 5, Issue 2, 2011, pp. 501–507
DOI: 10.4171/GGD/136

Published online: 2011-03-06

Powers in finite groups

Nikolay Nikolov[1] and Dan Segal[2]

(1) University of Oxford, UK
(2) University of Oxford, United Kingdom

If $G$ is a finitely generated profinite group then the verbal subgroup $G^{q}$ is open. In a $d$-generator finite group every product of $q$th powers is a product of $f(d,q)$ $q$th powers.

Keywords: Power subgroups, verbal width, profinite groups

Nikolov Nikolay, Segal Dan: Powers in finite groups. Groups Geom. Dyn. 5 (2011), 501-507. doi: 10.4171/GGD/136