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2004 Commutators and squares in free groups
Sucharit Sarkar
Algebr. Geom. Topol. 4(1): 595-602 (2004). DOI: 10.2140/agt.2004.4.595

Abstract

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.

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Sucharit Sarkar. "Commutators and squares in free groups." Algebr. Geom. Topol. 4 (1) 595 - 602, 2004. https://doi.org/10.2140/agt.2004.4.595

Information

Received: 2 January 2003; Revised: 25 March 2004; Accepted: 12 July 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1055.20025
MathSciNet: MR2077678
Digital Object Identifier: 10.2140/agt.2004.4.595

Subjects:
Primary: 20F12
Secondary: 57M07

Rights: Copyright © 2004 Mathematical Sciences Publishers

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