Residual finiteness conjecture for adjoint groups of quandles

From papers

A quandle is an algebraic structure with its standard quandle operation, and a quandle is residually finite if distinct elements can be separated by homomorphisms to finite quandles. Its adjoint group is the group generated by the quandle elements with the defining relations induced by the quandle operation. Residual finiteness conjecture. If a quandle is finitely presented and residually finite, then its adjoint group is residually finite. This would extend the residual-finiteness results established in the paper for free and link quandles, but no general proof is given.

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Sources & referencesView supporting material

Primary source

Valeriy Bardakov, Mohamed Elhamdadi and Mahender Singh, “Yang-Baxter Equation and Related Algebraic Structures”, arXiv:2506.23175 (2025).

Additional references

6 papers in this index state this conjecture (2008–2025). The statement above is taken from the most recent of them; the others are arXiv:2410.10152, arXiv:2202.08169, arXiv:1902.03082, arXiv:1202.5725, arXiv:0809.3420.

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