Volume 20, issue 7 (2020)

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The extrinsic primitive torsion problem

Khalid Bou-Rabee and W Patrick Hooper

Algebraic & Geometric Topology 20 (2020) 3329–3376
Abstract

Let Pk be the subgroup generated by k th powers of primitive elements in Fr, the free group of rank r. We show that F2Pk is finite if and only if k is 1, 2 or 3. We also fully characterize F2Pk for k = 2,3,4. In particular, we give a faithful 9–dimensional representation of F2P4 with infinite image.

Keywords
Burnside problem, primitive elements, characteristic subgroups, square-tiled surface
Mathematical Subject Classification 2010
Primary: 20F05, 20F65
Secondary: 20F38
References
Publication
Received: 11 December 2018
Revised: 30 October 2019
Accepted: 10 January 2020
Published: 29 December 2020
Authors
Khalid Bou-Rabee
Department of Mathematics
The City College of New York
New York, NY
United States
Department of Mathematics
The Graduate Center, CUNY
New York, NY
United States
https://sites.google.com/site/khalidmath/
W Patrick Hooper
Department of Mathematics
The City College of New York
New York, NY
United States
Department of Mathematics
The Graduate Center, CUNY
New York, NY
United States
http://wphooper.com/