# Corollary of Krull-Remak-Schmidt theorem for cancellation of powers

From Groupprops

## Statement

Suppose and are groups such that satisfies the following two conditions:

- the ascending chain condition on normal subgroups
- the descending chain condition on normal subgroups

Suppose is a positive integer such that the direct power (the external direct product of copies of ) is isomorphic to the direct power .

Then, and are isomorphic.

In particular, this result holds when is a finite group.