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arXiv · 1507.04168

The Zappa-Szep product of left-orderable groups

Fabienne Chouraqui
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Abstract

It is well-known that the direct product of left-orderable groups is left-orderable and that, under a certain condition, the semi-direct product of left-orderable groups is left-orderable. We extend this result and show that, under a similar condition, the Zappa-Szep product of left-orderable groups is left-orderable. Moreover, we find conditions that ensure the existence of a partial left and right invariant ordering (bi-order) in the Zappa-Szep product of bi-orderable groups and prove some properties.

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Fabienne Chouraqui. 2015-07-15. The Zappa-Szep product of left-orderable groups. https://arxiv.org/abs/1507.04168

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