Charakterisierung von orthogonalen Gruppen durch Beweglichkeitseigenschaften (Q1064542)

Properties of mobility have played a key role in many characterizations of orthogonal groups. The authors of the present paper give a characterization of the orthogonal and the special orthogonal groups for vector spaces over Euclidean fields. They use the order properties of this field to define half-spaces and flags. They show that a group of linear automorphisms satisfying a certain transitivity property on flags is either an orthogonal or a special orthogonal group.