A new Lindelöf topological group (Q2268852)

This paper is devoted to a problem posed by Arhangel'skii concerning the existence of a Lindelöf topological group with non-Lindelöf square. The approach is based on a recent deep result of J. Moore asserting that there exists an \(L\)-space in ZFC. It is shown that the subsemigroup of the product of \(\omega_1\)-many circles generated by the \(L\)-space constructed by J. Moore is again an \(L\)-space. This leads to a new example of a Lindelöf topological group. The question whether all finite powers of this group are Lindelöf remains open.