Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 4, Number 1 (2004), 595-602.
Commutators and squares in free groups
Let be the free group generated by and . In this article, we prove that the commutator of and is a product of two squares if and only if is even. We also show using topological methods that there are infinitely many obstructions for an element in to be a product of two squares.
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 595-602.
Received: 2 January 2003
Revised: 25 March 2004
Accepted: 12 July 2004
First available in Project Euclid: 21 December 2017
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Sarkar, Sucharit. Commutators and squares in free groups. Algebr. Geom. Topol. 4 (2004), no. 1, 595--602. doi:10.2140/agt.2004.4.595. https://projecteuclid.org/euclid.agt/1513882489