Amenable groups with a locally invariant order are locally indicable
Amenable groups with a locally invariant order are locally indicable
We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup of G , then a left-invariant total order …