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TitleOn small 3-nets embedded in a projective plane over a field
Author(s) Gábor P. Nagy, Nicola Pace
TypeArticle in Journal
AbstractAbstract In this paper, we investigate the projective embeddings of dual 3-nets realizing the groups C 3 × C 3 , C 2 × C 4 , or Alt 4 . We give a symbolically verifiable computational proof that every dual 3-net realizing the groups C 3 × C 3 and C 2 × C 4 is algebraic, namely, that its points lie on a plane cubic. Moreover, we present a computational approach for showing that the group Alt 4 cannot be realized if the characteristic of the ground field is zero. These results are fundamental for the complete classification of 3-nets embedded in a projective plane over a field.
Keywords3-Net, Dual 3-net, Embedding, Cubic curve, Groebner basis
URL http://www.sciencedirect.com/science/article/pii/S0097316513000940
JournalJournal of Combinatorial Theory, Series A
Pages1632 - 1641
Translation No
Refereed No