Remainders of topological and paratopological groups

In this paper, the remainders of topological and paratopological groups are discussed. Some conditions are given for a topological group G such that G or its compactification bG is separable and metrizable by the properties of the remainder b G ∖ G . Some properties are obtained for a paratopological group G such that the remainder b G ∖ G is a p-space or a Lindelöf space. They improve some results of A.V. Arhangelʼskiı̌ (2005) [1] and F. Lin (2011) [14], respectively, and also give partial answers to some questions posed by F. Lin (2011) [14] and C. Liu (2009) [16].