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Rapid decay for Wise’s non-Hopfian group

About 18 years old · traced to

Let GW=⟨a,b,c,s,t∣c=ab=ba, c2=sas−1=tbt−1⟩G_W=\langle a,b,c,s,t\mid c=ab=ba,\ c^2=sas^{-1}=tbt^{-1}\rangle. Then GWG_W has property RD (rapid decay).

References

Primary source

Oberwolfach Reports: 10.4171/OWR/2008/49, page 35

Additional references

Source: 10.4171/OWR/2008/49, page 35. Canonicalized from 1 source-backed detection(s); richer provenance is retained in the corpus artifact.

Posted · edited

Progress summary

Refreshed
Claimed solved

A published 2015 paper is reported to prove that Wise’s group has rapid decay, and no later challenge was found.

The problem asks whether the displayed Wise group has property RD. No proposer or original date is identified in the retrieved sources.

Known results

Barré and Pichot, 2015: proved property RD for Wise’s non-Hopfian group.

2015 published proof

Barré and Pichot’s article Property RD for D. Wise’s non Hopfian group, published in Annales de l’Institut Fourier 65 (2015), is cited by a 2016 survey as establishing the result. The retrieved material does not reproduce the proof or verify that its group presentation exactly matches the displayed presentation.

Current status (as of September 2026): The result is reported as proved by Barré and Pichot in 2015; no later objection or competing claim was found, but this automated report does not independently verify the proof.

Sources

Solutions 0

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