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2020 The extrinsic primitive torsion problem
Khalid Bou-Rabee, W Patrick Hooper
Algebr. Geom. Topol. 20(7): 3329-3376 (2020). DOI: 10.2140/agt.2020.20.3329

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.

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Khalid Bou-Rabee. W Patrick Hooper. "The extrinsic primitive torsion problem." Algebr. Geom. Topol. 20 (7) 3329 - 3376, 2020. https://doi.org/10.2140/agt.2020.20.3329

Information

Received: 11 December 2018; Revised: 30 October 2019; Accepted: 10 January 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194284
Digital Object Identifier: 10.2140/agt.2020.20.3329

Subjects:
Primary: 20F05 , 20F65
Secondary: 20F38

Keywords: Burnside problem , characteristic subgroups , primitive elements , square-tiled surface

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 7 • 2020
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