Geodesic
Commutators and squares in free groups
Sarkar, Sucharit1
1Stat-Math Unit, Indian Statistical Institute, Bangalore, India
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 595-602
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Let F2 be the free group generated by x and y. In this article, we prove that the commutator of xm and yn 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 F2 to be a product of two squares.

DOI : 10.2140/agt.2004.4.595
Keywords: Commutators, free groups, products of commutators

Sarkar, Sucharit  1

1 Stat-Math Unit, Indian Statistical Institute, Bangalore, India 
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Sarkar, Sucharit. Commutators and squares in free groups. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 595-602. doi: 10.2140/agt.2004.4.595

[1] M Akhavan-Malayeri, Powers of commutators as products of squares, Int. J. Math. Math. Sci. 31 (2002) 635

[2] R C Lyndon, M Newman, Commutators as products of squares, Proc. Amer. Math. Soc. 39 (1973) 267

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