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1Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary. E-mail: figula@math.klte.hu
Citation Information: Journal of Group Theory. Volume 12, Issue 3, Pages 419–429, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2008.087, November 2008
If the multiplication group Mult(L) of a connected simply connected 2-dimensional topological loop L is a Lie group, then Mult(L) is an elementary filiform Lie group ℱ of dimension n + 2 for some n ⩾ 2, and any such group is the multiplication group of a connected simply connected 2-dimensional topological loop L. Moreover, if the group topologically generated by the left translations of L has dimension 3, then L is uniquely determined by a real polynomial of degree n.
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