Universal norm of units in a Zp-extension ($N_{\infty }(E_n)={\bigcap }_{m\ge n}{N}_{m/n}(E_m)$)

These are units that lie in every finite-layer norm image, using the p-adic closures of the unit groups. Compactness makes this intersection the image of the norm inverse limit. Local and global universal norm subgroups need not coincide. In the cyclotomic main-conjecture proof, the finite defect of global units from universal norms is related by class field theory to invariants of the unramified module.