Recapturing semigroup compactifications of a group from those of its closed normal subgroups

We know that if S is a subsemigroup of a semitopological semigroup T, and stands for one of the spaces ,,, or ℒ, and (ϵ,T) denotes the canonical -compactification of T, where T has the property that (S)=(T)|s, then (ϵ|s,ϵ(S)¯) is an -compactification of S. In this paper, we try to show the converse of this problem when T is a locally compact group and S is a closed normal subgroup of T. In this way we construct various semigroup compactifications of T from the same type compactifications of S