  I discuss a family of statistical-mechanics models in which (some classes of)
elements of a finite group $G$ occupy the (directed) edges of a lattice; the
product around any plaquette is constrained to be the group identity $e$. Such
a model may possess topological order, i.e. its equilibrium ensemble has
distinct, symmetry-related thermodynamic components that cannot be
distinguished by any local order parameter. In particular, if $G$ is a
non-abelian group, the topological order may be non-abelian. Criteria are given
for the viability of particular models, in particular for Monte Carlo updates.
