Three-Dimensional Topological Loops with Solvable Multiplication Groups |
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Authors: | Agota Figula |
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Affiliation: | 1. Institute of Mathematics, University of Debrecen , Debrecen , Hungary figula@science.unideb.hu |
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Abstract: | We prove that each 3-dimensional connected topological loop L having a solvable Lie group of dimension ≤5 as the multiplication group of L is centrally nilpotent of class 2. Moreover, we classify the solvable non-nilpotent Lie groups G which are multiplication groups for 3-dimensional simply connected topological loops L and dim G ≤ 5. These groups are direct products of proper connected Lie groups and have dimension 5. We find also the inner mapping groups of L. |
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Keywords: | Multiplication groups of loops Solvable Lie group Topological transformation group |
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