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arXiv · 2002.04781

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

Casey Donoven
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Abstract

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

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Casey Donoven. 2020-02-12. Groups that are the union of two semigroups have left-orderable quotients. https://arxiv.org/abs/2002.04781

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