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Projectivity of a real projective line as a composition of cyclic projectivities. (English) Zbl 0696.51010

It is well-known that every projectivity of a projective line \(P_ 1(F)\) (F an arbitrary field) is a composition of two involutions. The author obtained a generalization of this theorem years ago [Zesz. Nauk. Geom. 11, 5-6 (1980; Zbl 0511.51025)] where two projectivities of the same order n were considered instead of two involutions, n being an arbitrary integer greater than 1. But \(F={\mathbb{C}}\) (the complex field) was assumed there. In the present paper the author considers the case of \(F={\mathbb{R}}\) (the real field) and obtains a weaker version of the above, proving that, for every positive integer \(n\neq 1\) or 3, every projectivity of \(P_ 1({\mathbb{R}})\) can be obtained as a product of either two projectivities of order n or a projectivity of order n and an involution.
Reviewer: A.Pasini

MSC:

51N15 Projective analytic geometry
14N05 Projective techniques in algebraic geometry

Citations:

Zbl 0511.51025
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