Abstract
LetJ be a finite inversive plane of odd orderq. If for at least one pointp ofJ the internal affine planeJ p is Desarguesian, thenJ is Miquelian. Other formulation: the finite Desarguesian affine plane of odd orderq has a unique one point extension; this extension is the Miquelian inversive plane of orderq. It follows that there is a unique inversive plane of orderq, withq∈{3, 5, 7}.
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