Lattice-ordered group
= Lattice-ordered group
{title2=$\ell\text{-group}$}
= l-group
{synonym}
An <ordered group> whose <partial order> is a <lattice>. Each pair has a <join> $f\vee g$ and a <meet> $f\wedge g$. Translations preserve these operations, for example $a(f\vee g)b=afb\vee agb$. Pointwise <maximum> and <minimum> make the <order automorphisms> of a chain into a lattice-ordered group.