Minimal determinants for the centres and topological centres of some

The algebraic centre of the uniformly continuous compactification G^UC of an abelian locally compact group G is G itself. There is a stronger result: if u commutes with just two (carefully chosen) elements of G^UC then u must be in G. The topological version of this idea is that if uv_j ® uv whenever v_j ® v in G^UC, then u Î G. In fact just one convergent net is absolutely necessary. Easy proofs of these facts will be given.