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In this article, we show that a group $G$ is the union of two propersubsemigroups if and only if $G$ has a nontrivial left-orderable quotient.Furthermore, if $G$ is the union of two proper semigroups, then there exists aminimum normal subgroup $N\unlhd G$ for which $G/N$ is left-orderable andnontrivial.

Groups that are the union of two semigroups have left-orderable quotients