Abstract
Free projective planes n? (generated by n points on a line and two points off that line) have been studied for some time. Until now, however, virtually nothing was known about the collineation groups of the planes itn except that the groups possessed no central collineations. In this paper, the collineation groups will be studied. We shall show that the collineation group of ir2 has three generators and exhibit them. Then, the orbit under this group of those points which lie on generating quadrilaterals will be determined. Finally, a subgroup H of the collineation group of 7r (n > 2) will be defined and it will be shown that there exists an integer m such that for every n > 2, Hn is generated by at most m collineations. It is the author's conjecture that Hn is in fact the full collineation group of itn, but the methods of the present paper do not seem to generalize to give this result.
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