# Isomorphic general linear groups not implies isomorphic rings

From Groupprops

## Statement

### Statement for

It is possible to have two commutative unital rings such that the general linear group of degree two is isomorphic to the general linear group of degree two , but and are *not* isomorphic as rings.

Two notable examples are:

- : See general linear group:GL(2,Z4).
- : See general linear group:GL(2,Z9).

(These are the only examples for finite discrete valuation rings, it seems).