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We consider three types of geometries of circles (Moebius plane, Laguerre plane and Minkowski plane, cf. [4) with respect to so-called multicentral automorphisms. An automorphism [phi] of any geometry of circles is central if it has a fix point P and [phi] becomes a central collineation in the derived projective plane M(P). For any central automorphism [phi] we try to establish the whole set of points R such that [phi] becomes a central collineation in M(R.). Than [phi] is called multicentral if this set contains at least two points. Moreover, [phi] is proper if existing of a point [R is not equal to P], is not caused by the fact that [phi] is central in M(P). There is no proper multicentral automorphism in a Moebius plane. The most interesting proper multicentral automorphisms are involutorial mappings: double homotheties in Minkowski planes, and (sigma, tau)homologies in Laguerre planes. We give some examples.
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Tom
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417--432
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Bibliogr. 14 poz.,
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- Faculty of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, ul. Żołnierska 14, 10-561 Olsztyn, Poland, jjakob@matman.uwm.edu.pl
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bwmeta1.element.baztech-article-BAT2-0001-0973