Abstract
We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem. This answers a well-known question of Collins from the early 1970’s.
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I would like to thank Alexander Olshanskii for his thoughtful comments on this work.
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The author acknowledges the support by the ERC-grant GroIsRan No. 725773.
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Darbinyan, A. Groups with decidable word problem that do not embed in groups with decidable conjugacy problem. Invent. math. 224, 987–997 (2021). https://doi.org/10.1007/s00222-020-01022-0
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DOI: https://doi.org/10.1007/s00222-020-01022-0