Commutators and squares in free groups
Group Theory
2014-10-01 v1
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.
Keywords
Cite
@article{arxiv.math/0409087,
title = {Commutators and squares in free groups},
author = {Sucharit Sarkar},
journal= {arXiv preprint arXiv:math/0409087},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-27.abs.html