Geodesic
Collineation Groups Containing Perspectivities
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 924-937

Voir la notice de l'article provenant de la source Cambridge University Press

Let P be a projective plane of finite order n and Γ a group of collineations of P. Gleason (6) and Wagner (10) have shown that if every point of P is the centre, and every line the axis, of a non-trivial perspectivity in Γ, then Γ contains a subgroup of order n2 which consists entirely of elations. It then follows that either P or its dual is a translation plane with respect to at least one line; in fact if Γ has no fixed elements, then P is desarguesian and Γ contains all elations of P. It was shown by Piper (7) and Cofman (4) that the hypotheses of Gleason and Wagner can be relaxed in certain cases, while the same conclusions hold. 
Dembowski, Peter. Collineation Groups Containing Perspectivities. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 924-937. doi: 10.4153/CJM-1967-085-0
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