Isomorphism versus commensurability for a class of finitely presented groups
Goulnara Arzhantseva, Jean‐François Lafont, Ashot Minasyan · Journal of Group Theory · 2013
Abstract. We construct a class of finitely presented groups within which 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 the first examples of such a contrastive complexity behavior with respect to the isomorphism problem.