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Coset intersection problem and application to 3nets
 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 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets 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 3nets. 
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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 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets 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 