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

Abstract

Abstract. We know that if S is a subsemigroup of a semitopological semigroup T , and Ᏺ stands for one of the spaces Ꮽᏼ, ᐃᏭᏼ, Ꮽᏼ, Ᏸ or ᏸᏯ, and ( , T Ᏺ ) denotes the canonical Ᏺ-compactification of T , where T has the property that Ᏺ(S) = Ᏺ(T ) |s , then ( |s , (S)) is an Ᏺ-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.