2026-09-24T06:45:08Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/72532 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

McCulloh, L., Carter, James Edgar 2014-12-17T23:17:44Z 2014-12-17T23:17:44Z 10000-01-01 1992 1992 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 b-th roots of unity, then it is known that $R\sb{t}(k,G)$ = $C(k)\sp{m}$ (the subgroup of $C(k)$ consisting of m-th 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. Made available in DSpace on 2014-12-17T23:17:44Z (GMT). No. of bitstreams: 1 9305482.pdf: 1608438 bytes, checksum: dd15b174003a8cf0d33667c465d2bb7d (MD5) Previous issue date: 1992 Embargo set by: Seth Robbins for item 72700 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 54 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992. http://hdl.handle.net/2142/72532 (UMI)AAI9305482 Mathematics Steinitz Classes of Tamely Ramified Nonabelian Extensions of Algebraic Number Fields of Degree P(3) text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.