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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 10, Pages 635-637
doi:10.1155/S0161171202013078

Powers of commutators as products of squares

M. Akhavan-Malayeri

Azzahra University, Vanak, Tehran 19834, Iran

Abstract

Let F be a free group and x,y be two distinct elements of a free generating set, then [x,y] n is not a product of two squares in F, and it is the product of three squares. We give a short combinatorial proof.