Homogeneous translation groups (Q2266227)

It is known that the translation group of a finite affine plane is transitive if in each direction the number of translations is the same. In this short note the author proves an analogous theorem for a topological affine plane with locally compact point set. He announces that his theorem will be used in a future publication to prove that the Moufang plane over the real octonians is the only compact projective plane admitting a group of dimension \(>40\).