Finite index subgroups without unique product in graphical small cancellation groups

Dominik Gruber; Alexandre Martin; Markus Steenbock

doi:10.1112/blms/bdv040

Finite index subgroups without unique product in graphical small cancellation groups

Dominik Gruber, Alexandre Martin, Markus Steenbock

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Abstract

For every integer k⩾1, we construct a torsion-free hyperbolic group without unique product all of whose subgroups up to index k are themselves non-unique product groups. This is achieved by generalizing a construction of Comerford to graphical small cancellation presentations, showing that for every subgroup H of a graphical small cancellation group there exists a free group F such that H*F admits a graphical small cancellation presentation.

Original language	English
Pages (from-to)	631–638
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	47
Issue number	4
DOIs	https://doi.org/10.1112/blms/bdv040
Publication status	Published - Aug 2015

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This is the peer reviewed version of the following article: Gruber, D., Martin, A. and Steenbock, M. (2015), Finite index subgroups without unique product in graphical small cancellation groups. Bulletin of the London Mathematical Society, 47: 631–638, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1112/blms/bdv040/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
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AB - For every integer k⩾1, we construct a torsion-free hyperbolic group without unique product all of whose subgroups up to index k are themselves non-unique product groups. This is achieved by generalizing a construction of Comerford to graphical small cancellation presentations, showing that for every subgroup H of a graphical small cancellation group there exists a free group F such that H*F admits a graphical small cancellation presentation.

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Finite index subgroups without unique product in graphical small cancellation groups

Abstract

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