Isomorphism versus commensurability for a class of finitely presented groups
classification
🧮 math.GR
math.LO
keywords
problemisomorphismclasscommensurabilityfinitelygroupspresentedconstruct
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We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability problem is solvable but the isomorphism problem is unsolvable. These are first examples of such a contrastive complexity behaviour with respect to the isomorphism problem.
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