On topological groups with remainder of character k

[EN] In [A.V. Arhangel’skii and J. van Mill, On topological groups with a first-countable remainder, Topology Proc. 42 (2013), 157-163] it is proved that the character of a non-locally compact topological group with a first countable remainder doesn’t exceed ω1 and a non-locally compact topological group of character ω1 having a compactification whose remainder is first countable is given. We generalize these results in the general case of an arbitrary infinite cardinal κ