Nonnormality of Čech-Stone-remainders of topological groups

It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper the question when a topological group G has a normal remainder. Under mild conditions on G we show that under the Continuum Hypothesis, if the Čech-Stone remainder G⁎ of G is normal, then it is Lindelöf.