Remainders in compactifications of topological groups

In this paper, we consider the following question: when does a topological group G have a Hausdorff compactification bG with a remainder belonging to a given class of spaces? We extend the results of A.V. Arhangelʹskii by showing that if a remainder of a non-locally compact topological group G has a countable open point-network or a locally G δ -diagonal, then G and the compactification bG of G are separable and metrizable.