Date Available
4-21-2017
Year of Publication
2017
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. David B. Leep
Abstract
The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5.
Digital Object Identifier (DOI)
https://doi.org/10.13023/ETD.2017.123
Recommended Citation
Sordo Vieira, Luis A., "ON P-ADIC FIELDS AND P-GROUPS" (2017). Theses and Dissertations--Mathematics. 43.
https://uknowledge.uky.edu/math_etds/43
