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Coset intersection problem and application to 3-nets
Title
Coset intersection problem and application to 3-nets.
Creator
Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
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...
Show moreIn 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.
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Date Issued
2012
PURL
http://purl.flvc.org/FAU/3355866
Subject Headings
Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
Format
Document (PDF)
study of divisors and algebras on a double cover of the affine plane
Title
A study of divisors and algebras on a double cover of the affine plane.
Creator
Bulj, Djordje., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
An algebraic surface defined by an equation of the form z2 = (x+a1y) ... (x + any) (x - 1) is studied, from both an algebraic and geometric point of view. It is shown that the surface is rational and contains a singular point which is nonrational. The class group of Weil divisors is computed and the Brauer group of Azumaya algebras is studied. Viewing the surface as a cyclic cover of the affine plane, all of the terms in the cohomology sequence of Chase, Harrison and Roseberg are computed.
Date Issued
2012
PURL
http://purl.flvc.org/FAU/3355618
Subject Headings
Algebraic number theory, Geometry, Data processing, Noncommutative differential geometry, Mathematical physics, Curves, Algebraic, Commutative rings
Format
Document (PDF)
Construction of combinatorial designs with prescribed automorphism groups
Title
Construction of combinatorial designs with prescribed automorphism groups.
Creator
Kolotoglu, Emre., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
In this dissertation, we study some open problems concerning the existence or non-existence of some combinatorial designs. We give the construction or proof of non-existence of some Steiner systems, large sets of designs, and graph designs, with prescribed automorphism groups.
Date Issued
2013
PURL
http://purl.flvc.org/fcla/dt/3360795
Subject Headings
Combinatorial designs and configurations, Finite geometries, Curves, Algebraic, Automorphisms, Mathematical optimization, Steiner systems
Format
Document (PDF)