Powers in finite groups

Nikolay Nikolov; Dan Segal

doi:10.4171/ggd/136

JournalsggdVol. 5, No. 2pp. 501–507

Powers in finite groups

Nikolay Nikolov
University of Oxford, UK
Dan Segal
University of Oxford, United Kingdom

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Abstract

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.

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Nikolay Nikolov, Dan Segal, Powers in finite groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 501–507

DOI 10.4171/GGD/136