Pride's JSJ conjecture for one-relator groups with torsion

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Let GG be a one-relator group with torsion that does not admit a free group as a free factor. Since one-relator groups with torsion are hyperbolic, GG has a JSJ-decomposition, meaning a canonical decomposition as a graph of groups whose edge groups are virtually-Z\mathbb{Z}. Pride's JSJ conjecture. Precisely one vertex group of the JSJ-decomposition of GG is a one-relator group with torsion; all other vertex groups are free groups. This is a concrete JSJ-theoretic formulation of the folk expectation that one-relator groups with torsion behave like free groups, and the paper's abstract indicates that it proves a slightly weaker version rather than this full assertion.

References

Primary source

Alan D. Logan, “The JSJ-decompositions of one-relator groups with torsion”, arXiv:1412.5357 (2016).

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