Korchmáros, G. and Nagy, Gábor Péter and Pace, N. (2014) 3-Nets realizing a group in a projective plane. JOURNAL OF ALGEBRAIC COMBINATORICS, 39 (4). pp. 939-966. ISSN 0925-9899
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Abstract
In a projective plane PG(2,K) defined over an algebraically closed field K of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky, arises 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. Urzua's 3-nets realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds true in characteristic p>0 apart from three possible exceptions Alt_4, Sym_4 and Alt_5.
Item Type: | Article |
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Uncontrolled Keywords: | embedding; projective plane; Cubic curve; Dual 3-net; 3-Net; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 06 Feb 2024 15:21 |
Last Modified: | 06 Feb 2024 15:21 |
URI: | http://real.mtak.hu/id/eprint/187713 |
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