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Coset intersection problem and application to 3-nets

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Date Issued:
2012
Summary:
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.
Title: Coset intersection problem and application to 3-nets.
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Name(s): Pace, Nicola
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: viii, 122 p. : ill.
Language(s): English
Summary: 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.
Identifier: 820724072 (oclc), 3355866 (digitool), FADT3355866 (IID), fau:3955 (fedora)
Note(s): by Nicola Pace.
Thesis (Ph.D.)--Florida Atlantic University, 2012.
Includes bibliography.
System requirements: Adobe Reader.
Mode of access: World Wide Web.
Subject(s): Finite fields (Algebra)
Mathematical physics
Field theory (Physics)
Curves, Algebraic
Held by: FBoU FAUER
Persistent Link to This Record: http://purl.flvc.org/FAU/3355866
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Owner Institution: FAU