Suppose you had two group presentations, and you know they are Euclidean groups, can you tell if they are isomorphic or not?
It has been suggested to me that it is probably possible to tell if they are isomorphic, but I can’t find a proof or come up with one myself.
Edit: Apologies for the confusion over what i mean by a Euclidean group. By Euclidean groups I mean discrete cocompact subgroups of isometries of euclidean space (of any dimension). This definition comes from 'Word Processing in Groups' by David B. A. Epstein et al, p.87.