Marginality is direct power-closed

This article gives the statement, and possibly proof, of a subgroup property (i.e., marginal subgroup) satisfying a subgroup metaproperty (i.e., direct power-closed subgroup property)
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Statement

Suppose $H$ is a marginal subgroup of a group $G$, and $\alpha$ is a finite or infinite cardinal. Then, in the direct power $G^{\alpha }$, $H^{\alpha }$ is a marginal subgroup. In fact, it is marginal for the same variety that $H$ is marginal in $G$.

Proof

The proof is straightforward.