Automorphisms of Projective Geometry in the sense of Klein

Details Automorphisms of Projective Geometry in the sense of Klein Automorphisms of Projective Geometry in the sense of Klein

2009-01-25

arxiv.org/abs/0901.3928v1

Mathematics

Group Theory

4 pages

Scientific paper

In this note, we prove that the automorphisms of Projective Geometry in the sense of Klein (i.e., the Klein geometry defined by the action of the group PGl_n on the set of 1-dimensional vector subspaces of an n+1-vector space) are the Staudt projectivities. This result is valid in arbitrary dimension and, as a consequence, we give a straightforward construction of the outer automorphism of S_6.

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