  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.
