# General linear group over algebraically closed field is divisible

From Groupprops

## Statement

Suppose is a field that is algebraically closed and is a general linear group of finite degree over , i.e., . Then, is a divisible group, i.e., for any and any positive integer , there exists (not necessarily unique) such that .

## Related facts

## Proof

The idea is to first conjugate to a Jordan canonical form matrix, then take the unique root of that.