Thesis--Universiteit van Amsterdam. / Published without thesis statement. Includes bibliographical references (p. [101]).

This thesis is concerned with the Galois groups of the root fields of the equations x[superscript]P - a = 0, (x[superscript]p - a)•(x[superscript]q - b) = 0 and (x[superscript]q - b) [superscript]p - a = 0, where p and q are distinct primes, and a and b are rationals. The correspondence of subflelds and subgroups is studied for each of the three cases. The field [formula omitted] formed by adjoining to the rational field F the elements [formula omitted and ⍺, a primitive pth root of unity, is shown to be the root field of x[superscript]p - a = 0, normal over F of degree p(p-l). The Galois group of [formula omitted] over F Is found to be the metacyclic group constructed from generators s and t subject to relations s[superscript]p = 1, t[superscript]p ⁻¹ = 1 and st = ts[superscript]r, where r is a primitive root modulo p, and where s is the automorphism which maps [formula omitted] onto [formula omitted] while t is the automorphism which maps ⍺. onto ⍺ [superscript]r. Various subgroups and corresponding subflelds are studied and nine theorems proven on their correspondences, illustrated with a partial lattice diagram. The field [formula omitted]where β is a primitive qth root of unity is shown to be the root field of (x[superscript]p - a)-(x[superscript]q - b) = 0 and the Galois group is proven to be the direct product of two of the type for the field [formula omitted]. The field [formula omitted] for i = 1, 2, 3 ... p, which is the root field of the equation (x[superscript]q - b) [superscript]p - a = 0 is studied and shown to have degree pq[superscript]p-(p-1)•(q-1). The Galois group is found to be generated by four independent generators: s, t, u, v subject to eleven defining relations. Here the elements s, t, u, v are the automorphisms which respectively map [formula omitted] onto [formular omitted], ⍺ onto ⍺[superscript r, [formula omitted] onto [formula omitted] β onto β [superscript]where w is a primitive root modulo q. A partial lattice diagram illustrates the correspondence of subgroups and subflelds. The thesis was carried out under the supervision of Dr. D. C. Murdoch. / Science, Faculty of / Mathematics, Department of / Graduate

Kwok, Tsz Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Historical remarks and main results --- p.6 / Chapter 1.2 --- Structure of the thesis --- p.8 / Chapter 2 --- Basic properties --- p.10 / Chapter 2.1 --- Existence of infinite convolution --- p.10 / Chapter 2.2 --- Properties --- p.16 / Chapter 2.3 --- Law of pure type --- p.17 / Chapter 3 --- Some results related to pure singularity --- p.20 / Chapter 3.1 --- The Pisot-Vijayaraghavan numbers --- p.20 / Chapter 3.2 --- The Salem numbers --- p.22 / Chapter 3.3 --- The weak separation condition --- p.23 / Chapter 4 --- A proof of almost everywhere absolute continuity --- p.30 / Chapter 5 --- Other results and problems --- p.37 / Chapter 5.1 --- Entropy of Bernoulli convolutions --- p.37 / Chapter 5.2 --- Dimensions --- p.40 / Chapter 5.3 --- Non PV numbers with bad behavior --- p.41 / Chapter 5.4 --- Open problems --- p.41 / Bibliography --- p.43

Thesis (doctoral)--Universität Marburg, 1911. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri, 1929. / Vita. "Lithoprinted." Includes bibliographical references (p. 27).

No description available.

No description available.

No description available.

Thesis (M.S.)--Oregon State College, 1952. / Typescript. Includes bibliographical references (leaf 21). Also available on the World Wide Web.

Thesis (M.A. 1971) from the Department of Mathematics, University of Adelaide.