Finite direct product-closed group property

Definition
A group property $$\alpha$$ is termed finite direct product-closed if it satisfies the following equivalent conditions:


 * 1) Whenever $$G_1$$ and $$G_2$$ are groups satisfying $$\alpha$$, the external direct product $$G_1 \times G_2$$ also satisfies $$\alpha$$.
 * 2) For any positive integer $$\alpha$$ and groups $$G_1,G_2,\dots,G_n$$ all of which satisfy $$\alpha$$, the external direct product $$G_1 \times G_2 \times \dots \times G_n$$ also satisfies $$\alpha$$.

Note that if the trivial group also satisfies $$\alpha$$, we say that $$\alpha$$ is strongly finite direct product-closed.