---
tag: NWADV41ZGV
kind: conjecture
name: Isomorphism problem of Coxeter groups
aliases: [isomorphism-problem-for-coxeter-groups]
sources:
  - wikipedia: en:79400576@r1310333104
    locator: Isomorphism problem of Coxeter groups
    note: adopted
    mention: wikipedia://en/79400576
    sections: [Statement]
same_as:
  wikidata: Q11301916
  wikipedia: Isomorphism problem of Coxeter groups
inventory: [5YVWHZB5TK]
---

## Statement

It is an unresolved problem in the mathematical field of group theory to determine whether or not two Coxeter groups (specified by their Coxeter diagrams) are isomorphic as abstract groups. Equivalently, the problem asks to determine, for a given Coxeter group $W$, the possible subsets $S$ of $W$ that are Coxeter generating sets for $W$ (that is, for which $(W , S)$ is a Coxeter system).