Algebraic & Geometric Topology

Commutators and squares in free groups

Sucharit Sarkar

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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.

Article information

Source
Algebr. Geom. Topol., Volume 4, Number 1 (2004), 595-602.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882489

Digital Object Identifier
doi:10.2140/agt.2004.4.595

Mathematical Reviews number (MathSciNet)
MR2077678

Zentralblatt MATH identifier
1055.20025

Subjects
Primary: 20F12: Commutator calculus
Secondary: 57M07: Topological methods in group theory

Keywords
Commutators free groups products of commutators

Citation

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


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