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Let $G$ be a group that is a set-theortic union of finitely many
proper subgroups. Cohn defined $\sigma(G)$ to be the least integer
$m$ such that $G$ is the union of $m$ proper subgroups.
Determining $\sigma$ is an open problem for most non-solvable
groups. In this paper we give a formula $\sigma(G)$, where $G$ is
a completely reducible group.
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