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.
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