# A characterization of Clifford parallelism by automorphisms

## TL;DR

This paper refines the understanding of Clifford parallelism in real projective space by establishing that it is uniquely characterized by invariance under groups of dimension at least 4, improving previous bounds.

## Contribution

The paper improves the known bound for the invariance of Clifford parallelism from 5 to 4, identifying 3 as the critical dimension for such invariance.

## Key findings

- Clifford parallelism is uniquely characterized by invariance under groups of dimension at least 4.
- The bound for the group dimension invariance is improved from 5 to 4.
- Examples exist of parallelisms with group invariance of dimension 3, marking it as the critical threshold.

## Abstract

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".