Ohnishi orderability criterion
= Ohnishi orderability criterion
{c}
A <group> admits a two-sided invariant <total order> exactly when every finite list of nonidentity elements can be signed so that the conjugation-invariant <semigroup> generated by the signed elements excludes the identity. A <compactness theorem> argument supplies a compatible global sign assignment. Omitting the conjugates changes the criterion to a different orderability problem.