Burnside Hall Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
On convex normal subgroups.
A subgroup H of a left ordered group (G, $le$) is $le$-convex if for any x,z $in$ H and y $in$ G the inequalities x $le$ y $le$ z imply y∈H. I will show that the family of $le$-convex normal subgroup can be finite of arbitrary size bigger than 1, countably infinite, or of cardinality continuum. I will also point out there is no countable universal left-orderable group.