Isomorphism problem of Coxeter groups

It is an unresolved problem in the mathematical field of group theory to determine whether or not two Coxeter groups are isomorphic as abstract groups. Equivalently, the problem asks to determine, for a given Coxeter group, the possible subsets of that are Coxeter generating sets for .
A slight generalization of the problem can be made by asking to find to all isomorphisms from one group onto the other.
In 2022, Yuri Santos Rego and Petra Schwer introduced a new framework to deal with the problem and asked more
related open questions motivated by it.