Volume 4, issue 1 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Commutators and squares in free groups

Sucharit Sarkar

Algebraic & Geometric Topology 4 (2004) 595–602

arXiv: math.GR/0409087

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.

Keywords
Commutators, free groups, products of commutators
Mathematical Subject Classification 2000
Primary: 20F12
Secondary: 57M07
References
Forward citations
Publication
Received: 2 January 2003
Revised: 25 March 2004
Accepted: 12 July 2004
Published: 5 November 2004
Authors
Sucharit Sarkar
Stat-Math Unit
Indian Statistical Institute
Bangalore
India