In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5. / by Nicola Pace. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / System requirements: Adobe Reader. / Mode of access: World Wide Web.
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_3955 |
| Contributors | Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Text, Electronic Thesis or Dissertation |
| Format | viii, 122 p. : ill., electronic |
| Rights | http://rightsstatements.org/vocab/InC/1.0/ |
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