Principal convex lattice subgroup
= Principal convex lattice subgroup
{title2=$\langle u\rangle_c=\{g:u^{-n}\le g\le u^n\text{ for some }n\}$}
For $u\ge1$ in a <lattice-ordered group>, the displayed set is the smallest <convex lattice subgroup> containing $u$. Products of two such bounds are bounded by a larger power of $u$; inversion and the <lattice> operations preserve the bounds. This gives an explicit test for membership.