Powers in finite groups

2009/09/25 by Dan Segal, Nikolay Nikolov, Segal, Dan +1
Mathematics · #20E20 #20F20 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E20 #msc:20F20

paper · pdf · doi:10.48550/arxiv.0909.4639

7 pages

arxiv created 2009/09/25 · arxiv updated 2009/12/01

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 qth powers is a product of f(d,q) qth powers.

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