Introduction to pseudo-ordered groups
We will give a definition, examples and basic properties of pseudo-ordered groups. These generalize partially-ordered groups. The pseudo-ordered groups have a compatible pseudo-order relation that may lack transitivity. Unlike partially-ordered groups, our groups can be finite and still admit a non-trivial pseudo-order. We will show necessary and sufficient conditions for a group to have a compatible pseudo-order. We also consider maximal pseudo-orders. We give a definition of a pseudo chain induced by a pseudo-order and characterize all pseudo chains on the group [special characters omitted]. We will calculate the number of non-isomorphic pseudo-orders on [special characters omitted] for n < 24.
Cruz Quinones, Maria Dolores, "Introduction to pseudo-ordered groups" (2009). ETD Collection for University of Texas, El Paso. AAI1473856.