Abstract
(Communicated by R. M. Guralnick)Abstract. If the multiplication group MultðLÞ of a connected simply connected 2-dimensionaltopological loop L is a Lie group, then MultðLÞ is an elementary filiform Lie group F of di-mension nþ2 for some nd2, and any such group is the multiplication group of a connectedsimply connected 2-dimensional topological loop L. Moreover, if the group topologicallygenerated by the left translations of L has dimension 3, then L is uniquely determined by areal polynomial of degree n.
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