Classification of Groups Which Admit a Finite Number of Distinct Right-Orders |
| |
Authors: | A. Kirk |
| |
Affiliation: | 1. School of Mathematical Sciences, Queen Mary, University of London , London, UK a.kirk@qmul.ac.uk |
| |
Abstract: | Tararin has shown that a non-Abelian group G admits a nonzero finite number of distinct right-orders if and only if G is equipped with a Tararin-type series of some length n. Further, a group which has a Tararin-type series of length n admits 2 n right-orders. It is known that a group has two right-orders if and only if it is torsionfree Abelian of rank 1. Here we completely classify the groups which admit either four or eight right-orders. |
| |
Keywords: | Right-orderable group System of convex subgroups Torsionfree Abelian group of rank 1 |
|
|