Prime convex lattice subgroup
= Prime convex lattice subgroup
A proper <convex lattice subgroup> $P$ is prime when $a,b\ge1$ and $a\wedge b=1$ imply $a\in P$ or $b\in P$. Equivalently the ordered right cosets of $P$ form a <totally ordered set>. Prime refers to this order property, and does not require a <normal subgroup> or prime index.