Abstract
We investigate several series of closure theorems which can be considered as properties of projectivities in general projective planes. Most of them postulate that the projectivity α= [11R213] ... [12n-1R011] (indices modulo 2n) or α2 should be the identity if the lines 1i or the points Rj satisfy special incidence conditions. This way of construction leads to some generalizations of well-known propositions as for example the great and little Desarguesian, the Pappian theorem and some other interesting cases. We prefer the synthetic method to determine the class of planes in which these closure theorems hold. In one case the analytic method only seems to be successful.
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