Adjacency preserving mappings on point-line geometries

In certain point-line geometries $G = (P, ℒ)$ , $G^{'} = (P^{'}, ℒ^{'})$ , which include dense near polygons and the geometry of Hermitian matrices, any adjacency preserving mapping $φ : P \to P^{'}$ satisfying

\exists p, q \in P : d (p, q) = d (p^{φ}, q^{φ}) = diam (G),

is an isomorphism between $G$ and $φ (G)$ .

Mathematical Subject Classification 2000

Primary: 15A57, 51A50

Milestones

Received: 18 September 2005

Accepted: 22 November 2005

Authors

Wen-ling Huang

Vol. 3, No. 1, 2006

Wen-ling Huang

Abstract

Mathematical Subject Classification 2000

Milestones

Authors