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.
|Title of host publication||Infinite Group Theory|
|Subtitle of host publication||From The Past To The Future|
|Publisher||World Scientific Publishing Co. Pte Ltd|
|Number of pages||7|
|State||Published - 26 Dec 2017|
Bibliographical notePublisher Copyright:
© 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
ASJC Scopus subject areas
- Mathematics (all)