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A New Construction Of Subgroups Inducing Isomorphic Representations., Patricia Wright Beaulieu
A New Construction Of Subgroups Inducing Isomorphic Representations., Patricia Wright Beaulieu
LSU Historical Dissertations and Theses
This dissertation provides a method to construct infinite families of triples ($H\sb{i},H\sbsp{i}{\prime},G\sb{i}$) consisting of two non-conjugate subgroups $H\sb{i}$ and $H\sbsp{i}{\prime}$ of a finite group $G\sb{i}$ whose trivial representations induce isomorphic representations of $G\sb{i}$. Such triples are important in number theory, differential geometry, and group theory.
A New Condition For Arithmetic Equivalence., Donna Joy Stuart
A New Condition For Arithmetic Equivalence., Donna Joy Stuart
LSU Historical Dissertations and Theses
Two algebraic number fields K, K$\sp\prime$ are said to be arithmetically equivalent if every prime number p has the same splitting type in K as in K$\sp\prime$. Many equivalent formulations of arithmetic equivalence are known. The best-known of these is: K and K$\sp\prime$ are arithmetically equivalent if and only if their Dedekind zeta functions coincide. This dissertation provides a surprising new formulation: K and K$\sp\prime$ are arithmetically equivalent if and only if for all prime numbers p, outside a given set of density zero, the number $g\sb K (p)$ of prime factors of p in K is equal to the …
On The Construction And Application Of Certain Special Polarizations In Nilpotent Lie Algebras., James Donald Moss Jr
On The Construction And Application Of Certain Special Polarizations In Nilpotent Lie Algebras., James Donald Moss Jr
LSU Historical Dissertations and Theses
This dissertation arose from efforts to prove the following conjecture, which generalizes to nilpotent Lie groups a weak form of the classical Paley-Wiener theorem for $\IR\sp{n}$: Let N be any connected, simply connected nilpotent Lie group with unitary dual N, and let $\varphi\in L\sbsp{c}{\infty}(N)$. Suppose that there exists a subset E $\subset$ N of positive Plancherel measure such that $\\varphi(\pi)$ = 0 for all $\pi\in$ E, where $\\varphi(\pi)$ is the operator-valued Fourier transform of $\varphi$. Then $\varphi$ = 0 almost everywhere on N. The writer has been able to prove a slightly weakened form of the conjecture for a large …
Some Results On Minors For Graphs And Matroids., Lawrence Alan Wargo
Some Results On Minors For Graphs And Matroids., Lawrence Alan Wargo
LSU Historical Dissertations and Theses
This dissertation solves some problems relating to the theory of graphs. The first type of problem considered concerns the structure of various classes of graphs which arise naturally from outerplanar graphs. These problems are motivated by Chartrand and Harary's well-known characterization of outerplanar graphs. This theorem states that K$\sb4$ and K$\sb{2,3}$ are the only non-outerplanar graphs for which both G$\\$e, the deletion of the edge e from the graph G, and G/e, the contraction of the edge e, are outerplanar for all edges e of G. Following Gubser's characterization of almost-planar graphs, we begin our study of graphs related to …