On Perspectivities of finite projective plannes.

In a projective plane π containing only a finite number of points it is a sufficient condition, on which the Theorem of Desargues for two triangles of π is valid, that the collineation group II characterizing π is sufficiently large. The purpose of this article is to introduce a series of theorems on the 'largeness' of the group II of π and their interesting proofs almost due to J.ANDRE [1], A.WARGNER [6], F.C.PIPER [5] and so on. 0. A projective plane π ia a set of points, of which certain sudsets are called lines: Writing P∈π, p〓π to indicate that P is a point of π, p is a line of π respectively, we may appeal to AXIOMS. 1) ∃P=p⌒q with p≠9 | P∈p,q for p,q 2) ∃p=P〓Q with P≠Q | p∋P,Q for P,Q 3) [P,Q∈p