Abstract
Given a circle \(C\) of an inversive plane \({\mathcal {I}}\) of order \(n\), the remaining circles are partitioned into three types according to the number of intersection points with \(C\). Let \({\mathcal {S}}\) be the incidence structure formed by the points of \({\mathcal {I}}\) and any two types of circles. It is proved that with some additional requirements, \({\mathcal {I}}\) is the only inversive plane of order \(n\) having \({\mathcal {S}}\) as an induced substructure.
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The author would like to thank Joseph A. Thas for his proofreading of a draft of this article.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
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Hui, A.M.W. Extending some induced substructures of an inversive plane. Des. Codes Cryptogr. 79, 611–617 (2016). https://doi.org/10.1007/s10623-015-0083-5
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DOI: https://doi.org/10.1007/s10623-015-0083-5