Linearly ordered group

Group with translationally invariant total order; i.e. if a ≤ b, then ca ≤ cb

In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant. This may have different meanings. We say that (G, ≤) is a:left-ordered group if ≤ is left-invariant, that is a ≤ b implies ca ≤ cb for all a, b, c in G, right-ordered group if ≤ is right-invariant, that is a ≤ b implies ac ≤ bc for all a, b, c in G, bi-ordered group if ≤ is bi-invariant, that is it is both left- and right-invariant.

This keyword could refer to multiple things. Here are some suggestions: