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The JSJ-decompositions of one-relator groups with torsion

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Abstract

In this paper we use JSJ-decompositions to formalise a folk conjecture recorded by Pride on the structure of one-relator groups with torsion. We prove a slightly weaker version of the conjecture, which implies that the structure of one-relator groups with torsion closely resemble the structure of torsion-free hyperbolic groups.

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Notes

  1. We only need orbifold vertices to define JSJ-decompositions; they are not mentioned anywhere else in this paper. Therefore, the interested reader is referred to Bowditch [1] for a formal definition.

  2. The precise equivalence relation can be found in Bowditch’s paper [1, Section 6].

  3. See Question 2 from the introduction.

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Acknowledgments

The author would like to thank his Ph.D. supervisor, Stephen J. Pride, and Tara Brendle for many helpful discussions about this paper, and Jim Howie for suggestions regarding a preprint. He would also like to thank an anonymous referee of another paper [13] for the suggestion to apply the ideas of Kapovich–Weidmann to prove Theorem 2, which led to this paper.

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  1. School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland, UK

    Alan D. Logan

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  1. Alan D. Logan
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Correspondence to Alan D. Logan.

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Logan, A.D. The JSJ-decompositions of one-relator groups with torsion. Geom Dedicata 180, 171–185 (2016). https://doi.org/10.1007/s10711-015-0097-1

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