Abstract
Abstract Let P be a topological parallelism of the real projective 3-space PG3ℝ. We investigate the group AutP of all collineations of PG3ℝ leaving P invariant. We prove that AutP is a Lie group whose dimension is at most 6. The main result of the article says: if the dimension equals 6, then P is a Clifford parallelism. Furthermore, we show that there are no topological parallelisms in PG3ℝ with a 5-dimensional group.
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