The object of this paper is to find a necessary and sufficient condition for the groups $G_1, G_2, ..., G_n$ so that every normal subgroup of the product $\prod_{ i=1}^{ n} G_i$ is of the type $\prod_{ i=1}^{ n} N_i$ with $N_i \trianglelefteq G_i$, $i=1,2, ..., n$. As a consequence we obtain a well-known result due to R. Remak about centreless completely reducible groups having finitely many direct factors.
Categories: math.GR