International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 10, Pages 635-637

Powers of commutators as products of squares

M. Akhavan-Malayeri

Azzahra University, Vanak, Tehran 19834, Iran

Received 2 May 2001; Revised 13 January 2002

Copyright © 2002 M. Akhavan-Malayeri. 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.


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.