Files in this item
Files  Description  Format 

application/pdf 9305482.pdf (2MB)  (no description provided) 
Description
Title:  Steinitz Classes of Tamely Ramified Nonabelian Extensions of Algebraic Number Fields of Degree P(3) 
Author(s):  Carter, James Edgar 
Doctoral Committee Chair(s):  McCulloh, L., 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  Let L/k be a finite extension of algebraic number fields of degree n with rings of integers ${\cal D}\sb{L}$ and ${\cal D}\sb{k}$. As an ${\cal D}\sb{k}$module ${\cal D}\sb{L}$ is finitely generated and torsion free and thus can be written as a direct sum of $n  1$ copies of ${\cal D}\sb{k}$ and a fractional ideal ${\cal J}$ of k. The class $c\ell({\cal J})$ of ${\cal J}$ in the ideal class group C(k) of k is the Steinitz class C(L,k) of ${\cal D}\sb{L}$. Now let G be a finite group of order n. As L varies over all normal extensions of k such that Gal(L/k) $\simeq$ G, C(L,k) varies over a subset of C(k). These are the realizable classes of k with respect to G which we denote by R(k,G). If we consider only tamely ramified extensions then we denote this set by $R\sb{t}(k,G)$. If G is an abelian group with exponent b, and k contains the multiplicative group of bth roots of unity, then it is known that $R\sb{t}(k,G)$ = $C(k)\sp{m}$ (the subgroup of $C(k)$ consisting of mth powers of elements of $C(k))$ where m is a positive rational integer which depends on the structure of G. We obtain a partial generalization of this result in the sense that if n = $p\sp3$ where p is an odd prime then we can remove the restriction that G be an abelian group. 
Issue Date:  1992 
Type:  Text 
Description:  54 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1992. 
URI:  http://hdl.handle.net/2142/72532 
Other Identifier(s):  (UMI)AAI9305482 
Date Available in IDEALS:  20141217 
Date Deposited:  1992 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois