We construct in the K matrix formalism concrete examples
of symmetry enriched topological phases, namely intrinsically topological
phases with global symmetries. We focus on the Abelian and non-chiral
topological phases and demonstrate by our examples how the interplay between
the global symmetry and the fusion algebra of the anyons of a topologically
ordered system determines the existence of gapless edge modes protected by the
symmetry and that a (quasi)-group structure can be defined among these phases.
Our examples include phases that display charge fractionalization and more
exotic non-local anyon exchange under global symmetry that correspond to
general group extensions of the global symmetry group.