Unit-surjectivity criterion for a trivial finite ray class group
= Unit-surjectivity criterion for a trivial finite ray class group
For a modulus with no infinite component, suppose the ordinary <ideal class group> is trivial. Then the <ray class group> is trivial exactly when the global <unit group> maps surjectively onto the product of local unit residue groups at the finite modulus. Negative real units are allowed: positivity restrictions occur only when the modulus includes the corresponding real places.