# Homology group for trivial group action commutes with direct product in second coordinate

From Groupprops

## Statement

### For two groups

Suppose is a group and and are (possibly isomorphic, possibly non-isomorphic) abelian groups. Let be a nonnegative integer. Denote by , , and the homology groups for trivial group action of on , and the external direct product respectively. Then, there is a canonical isomorphism: