  A subgroup $G$ of a product $\prod\limits_{i\in\mathbb{N}}G_i$ is
\emph{rectangular} if there are subgroups $H_i$ of $G_i$ such that
$G=\prod\limits_{i\in\mathbb{N}}H_i$. We say that $G$ is \emph{weakly
rectangular} if there are finite subsets $F_i\subseteq \mathbb{N}$ and
subgroups $H_i$ of $\bigoplus\limits_{j\in F_i} G_j$ that satisfy
$G=\prod\limits_{i\in\mathbb{N}}H_i$. %We say that $G$ is a \emph{subdirect
product} of the family $\{G_i\}_{i\in I}$ if $G$ is weakly rectangular and
%$G\cap\bigoplus\limits_{i\in I} G_i=\bigoplus\limits_{i\in\mathbb{N}}H_i$. In
this paper we discuss when a closed subgroup of a product is weakly
rectangular. Some possible applications to the theory of group codes are also
highlighted.
