It seems like there are a decent number of questions about placing some sort of order on a group. I would like to tag these questions to better organize them, but I'm not sure what to call the tag.
The phrase "ordered group" to me implies that we have a total order $\leq$ which is preserved under both left and right multiplication. But people could be asking questions about partial or lattice orders, or the ordering could be preserved only under right multiplication, etc.
Creating separate tags for each of these niche subjects seems like overkill to me, so is the standard to just call it [ordered-groups] and assume people will be able to figure out the ambiguity? One alternative would be to call it [partially-ordered-groups] and hope that people realize that even if they have a stronger restriction, they can still use the tag.
- Order Preserving Isomorphism
- isomorphism between divisible, totally ordered, abelian groups
- Embedding $\omega_1$ into the direct sum/product of $\Bbb R$'s and $\Bbb N$'s
- What motivates the definition of "Periodic" group action
(These were taken by searching for questions tagged as both [group-theory] and [order-theory]. I filtered out the ones asking about the order of a group.)