Density in locally compact topological groups

We introduce some notions of density in a locally compact topological group G which extend some notions in discrete semigroups in which density is based on nets of finite sets. The new notions are based on nets of compact sets. We consider that the LUC -compactification of G is a set of z-filters on LUC ( G ) and obtain new information about the algebraic structure of this form. Also we present a version of Schurʹs Theorem in a locally compact topological group.