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We prove that among the quasi-simple Lie groups only the group SL 4 (ℝ) occurs as the multiplication group of 3-dimensional connected topological loops L. These loops L are homeomorphic to the sphere S 3 . Moreover, there does not exist any connected topological loop having an at most 8-dimensional quasi-simple Lie groups as its multiplication group.

Quasi-simple Lie groups as multiplication groups of topological loops