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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some constructions of infinite Möbius planes


Author: Nicholas Krier
Journal: Trans. Amer. Math. Soc. 254 (1979), 95-115
MSC: Primary 51B10
MathSciNet review: 539909
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Abstract: New infinite Möbius planes are constructed using transfinite induction. Any infinite affine plane A can be embedded in a Möbius plane M and the construction allows some groups of perspectivities of A to be extended to automorphism groups of M. Given $ \left\{ {{A_\alpha },\,\alpha \, \in \,J} \right\}$, an infinite collection of s affine planes each of order s, there exist a Möbius plane M and a bijection b from J to the point set of M so that for each $ \alpha \, \in \,J,\,{M_{b\left( \alpha \right)}}$ is isomorphic to $ {A_\alpha }$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0539909-0
PII: S 0002-9947(1979)0539909-0
Keywords: Möbius plane, affine plane, transfinite induction, ovoid, automorphism group, semioval
Article copyright: © Copyright 1979 American Mathematical Society