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Commutators and squares in free groups

Sucharit Sarkar
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Abstract

Let F_2 be the free group generated by x and y. In this article, we prove that the commutator of x^m and y^n is a product of two squares if and only if mn is even. We also show using topological methods that there are infinitely many obstructions for an element in F_2 to be a product of two squares.

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Sucharit Sarkar. 2004-09-06. Commutators and squares in free groups. https://doi.org/10.2140/agt.2004.4.595

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