# Thread:

1. ## direct products

Show that the center of a direct product is the direct product of centers:
$Z(G_1$ x $G_2$ x ... x $G_n)=Z(G_1)$ x $Z(G_2)$ x ... x $Z(G_n)$.
Deduce that a direct product of groups is abelian if and only if each of the factors is abelian.

I know that $G_1$x $G_2$ x ... x $G_n$ is isomorphic to $G_1G_2...G_n$.
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