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.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The author was supported by an EPSRC research studentship. The author is grateful to her former research supervisor, P. H. Kropholler, for many helpful and interesting discussions.
Notes
Communicated by D. Macpherson.