There are three kinds of the Benz planes: Mobius planes, Laguerre planes and Minkowski planes [2, 3, 7]. In any Benz plane an automorphism φ is central if φ has a fixed point P and becomes a central collineation in the projective derived plane induced by P. Such central automorphisms have been considered by many authors (cf. [8,13, 11, 12, 10]), in particular the automorphism groups were classified. Usually product of two central collineations without common center or common axis is not central. But in some special cases it is central [4]. In this paper we apply theorems concerning such special cases - to the Benz planes.
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