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 satisfied.
| Original language | English |
|---|---|
| Title of host publication | Infinite Group Theory |
| Subtitle of host publication | From The Past To The Future |
| Publisher | World Scientific Publishing Co. Pte Ltd |
| Pages | 43-49 |
| Number of pages | 7 |
| ISBN (Electronic) | 9789813204058 |
| ISBN (Print) | 9789813204041 |
| State | Published - 26 Dec 2017 |
Bibliographical note
Publisher Copyright:© 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
ASJC Scopus subject areas
- General Mathematics