# Commensurability of the spherical Artin groups F4 and H4

- Reference: `kourovka-21-128-commensurability-of-the-spherical-artin-groups-f4-and-h4`
- Page: https://theoremdb.org/statements/kourovka-21-128-commensurability-of-the-spherical-artin-groups-f4-and-h4
- Record maturity: Reviewed problem

## Problem

Two groups G1 and G2 are said to be commensurable if there exist finiteindex subgroups H1 ⩽ G1 and H2 ⩽ G2 (not necessarily of the same index) such that H1 ∼= H2. Let A[F4 ] and A[H4 ] denote the Artin groups of spherical types F4 and H4, respectively. Are these two groups commensurable? This is the most difficult case in the classification of Artin groups of spherical type up to commensurability. This is Kourovka Notebook Problem \(21.128\).

## Status

The reviewed record remains open.

## Work

### Working on this

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## References

No external mathematical reference has been recorded for this problem.