# Corollary of Krull-Remak-Schmidt theorem for cancellation of factors in direct product

From Groupprops

## Statement

If , , and are groups of finite composition length such that the external direct products and are isomorphic, i.e., , then .

## Related facts

- Krull-Remak-Schmidt theorem
- Corollary of Krull-Remak-Schmidt theorem for cancellation of powers
- Direct product is cancellative for finite groups