Thesis (MSc) -- Stellenbosch University, 2004. / ENGLISH ABSTRACT: In this thesis we give a survey of research done on a problem on subnormal subgroups in factorized groups G = AB, where A and B are two subgroups of G with H a subgroup of A n B which is subnormal in both A and B. It is of interest to know whether or not such a subgroup H will also be subnormal in G. During the past twenty five to thirty years some positive results were obtained in the case where G is a finite group. This was mainly due to work done by Maier and Wielandt, with results by Sidki and Casolo following shortly afterwards. Counterexamples in the case of infinite groups seemed to be extremely hard to construct. For the infinite group case, some positive results were obtained through contributions by amongst others Stonehewer, Franciosi, de Giovanni and Sysak. Most recently some alternative proofs were given by Fransman. / AFRIKAANSE OPSOMMING: In hierdie tesis poog ons om 'n oorsig te gee van navorsing uitgevoer oor 'n probleem rakende subnormale ondergroepe van 'n groep G = AB wat uitgedruk kan word as 'n produk van twee ondergroepe A en B. Daar word gepoog om te bepaal vir watter klasse van groepe dit volg dat as die ondergroep H van A se deursnede met B subnormaal is in beide A en B, sal dit impliseer dat H ook subnormaal in die groep G sal wees. Gedurende die afgelope vyf-en-twintig na dertig jaar is positiewe resultate bewys VIr eindige sodanige groepe deur veralouteurs soos Maier en Wielandt, gevolg deur Sidki en Casolo. Dit blyk dat dit nie maklik is om teenvoorbeelde te vind vir die oneindige geval nie. Daar is wel positiewe resultate gelewer vanweë bydraes deur onder andere Stonehewer, Franciosi, de Giovanni en Sysak. Meer onlangs is ook alternatiewe bewyse gegee deur Fransman.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Ph.D.)--University of Western Australia, 2004.

Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1940. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1940. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.A.)--The University of North Carolina at Greensboro, 2008. / Directed by Paul Duvall; submitted to the Dept. of Mathematical Sciences. Title from PDF t.p. (viewed Aug. 25, 2009). Includes bibliographical references (p. 35-36).

Thesis (Ph. D.) -- California Institute of Technology, 2010. / Title from home page (viewed 06/21/2010). Advisor and committee chair names found in the thesis' metadata record in the digital repository. Includes bibliographical references.

by Li King Hung. / Thesis submitted in: July, 1998. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 54-56). / Abstract also in Chinese. / Chapter 1 --- Description of the Number Field Sieve --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.2 --- Outline of the algorithm --- p.8 / Chapter 2 --- Algebraic knowledge --- p.17 / Chapter 2.1 --- Factorization of an ideal over the class of ideals --- p.17 / Chapter 2.2 --- Existence of the square roots of an element in the ring of algebraic integers --- p.26 / Chapter 3 --- Run time analysis and Practical result --- p.31 / Chapter 3.1 --- Relation between sieving over X and finding the linear dependencies --- p.32 / Chapter 3.2 --- Relation between the size of a factor base and finding the linear dependencies --- p.34 / Chapter 3.3 --- Practical consideration --- p.36 / Chapter 4 --- Improvement of the algorithm --- p.38 / Chapter 4.1 --- Quadratic characters --- p.38 / Chapter 4.2 --- Finding the square root --- p.40 / Chapter 4.3 --- Solving the linear system of equation --- p.42 / Chapter 4.4 --- Reusing the computation --- p.47 / Chapter 4.5 --- Using more general purpose data --- p.50 / Chapter 4.6 --- Examples --- p.51 / Chapter 4.6.1 --- "A 18-digit example,761260375069630873" --- p.52 / Chapter 4.6.2 --- "A 23-digit example, 16504377514594481520559" --- p.52 / Bibliography