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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/50050 |
| Date | 04 1900 |
| Creators | Oberholzer, Ria M |
| Contributors | Fransman, A, Stellenbosch University. Faculty of Science. Department of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | vi, 67 pages |
| Rights | Stellenbosch University |
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