  There has been interest recently concerning when a left ordered group is
locally indicable. Bergman and Tararin have shown that not all left ordered
groups are locally indicable, but all known examples contain a nonabelian free
subgroup. We shall show for a large class of groups not containing a nonabelian
free subgroup, that any left ordered group in this class is locally indicable.
Specifically this class is the smallest class of groups containing NS and
Thompson's group of piecewise linear homeomorphisms of the unit interval, and
is closed under taking subgroups, quotient groups, extensions and directed
unions; here NS is the class of groups which do not contain a nonabelian
subsemigroup. We shall also show that certain free products with an amalgamated
cyclic subgroup are left orderable.
