The Zappa-Szep product of left-orderable groups
Group Theory
2021-05-27 v3
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.
Keywords
Cite
@article{arxiv.1507.04168,
title = {The Zappa-Szep product of left-orderable groups},
author = {Fabienne Chouraqui},
journal= {arXiv preprint arXiv:1507.04168},
year = {2021}
}
Comments
This is a final version after some changes