Continuity in G∗

For a discrete group G, we consider βG, the Stone–Čech compactification of G, as a right topological semigroup, and G∗=βG⧹G as a subsemigroup of βG. We study the mappings λp∗ :G∗→G∗and μ∗ :G∗→G∗, the restrictions to G∗ of the mappings λp :βG→βG and μ :βG→βG, defined by the rules λp(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λp∗ or μ∗ at some point of G∗ implies the existence of a P-point in ω∗.