# Isomorphic special linear groups implies isomorphic fields

From Groupprops

## Statement

Suppose are fields and is a natural number. Then, if the special linear groups and are isomorphic groups, and must be isomorphic as fields.

Note that the case is different, because is the trivial group for any field .

## Related facts

- Isomorphic special linear groups implies isomorphic fields
- Isomorphic general affine groups implies isomorphic fields
- Isomorphic unitriangular matrix groups implies isomorphic fields