On Subplanes of Miquelian Inversive Planes

Abstract.

Precisely the Miquelian inversive planes allow an algebraic representation based on a quadratic field extension. Their automorphism group is also well understood. This paper shows that all subplanes of a Miquelian plane of finite order are induced by what is called a planar automorphism of the given plane. We will prove this by revisiting the algebraic representation of Miquelian planes, and extending it to a plane-subplane representation.