Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

A characterization of Clifford parallelism by automorphisms

Rainer Löwen

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Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms admitting a group of dimension 3 are known, so 3 is the “critical dimension”.

Article information

Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 1 (2019), 43-46.

Received: 17 February 2017
Accepted: 23 March 2017
First available in Project Euclid: 26 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51H10: Topological linear incidence structures 51A15: Structures with parallelism 51M30: Line geometries and their generalizations [See also 53A25]

Clifford parallelism automorphism group topological parallelism


Löwen, Rainer. A characterization of Clifford parallelism by automorphisms. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 1, 43--46. doi:10.2140/iig.2019.17.43.

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