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Fano Configurations in Subregular Planes


Abstract


In this article a wide variety of odd-order translation planes, constructedfrom Desarguesian planes by multiple derivation, are shown to admit Fanoconfigurations. For example, we show that subregular planes of odd order q^{2} obtained by the replacement of at most (q-1)/4 disjoint nets admitFano configurations. Further, for s odd and greater than 1, any subregularplane of order q^{2} can be embedded into a subregular plane of order q^{2s} that contains the original plane as a subplane and admits Fano configurations.


DOI Code: 10.1285/i15900932v28n2p69

Keywords: Fano subplane; derivation; replaceable net

Classification: 51E23; 51A40

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