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

Powers of commutators as products of squares

Azzahra University, Vanak, Tehran 19834, Iran

Received 2 May 2001; Revised 13 January 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.