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On subnormal subgroups in factorized groups
Thesis (MSc) -- Stellenbosch University, 2004.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867614081907687424 |
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| access_status_str | Open Access |
| author | Oberholzer, Ria M. |
| author2 | Fransman, A. |
| author_browse | Fransman, A. Oberholzer, Ria M. |
| author_facet | Fransman, A. Oberholzer, Ria M. |
| author_sort | Oberholzer, Ria M. |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc) -- Stellenbosch University, 2004. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/50050 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:22.874Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/50050 On subnormal subgroups in factorized groups Oberholzer, Ria M. Fransman, A. Stellenbosch University. Faculty of Science. Department of Mathematical Sciences. Group theory Factorization (Mathematics) 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 re 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. 2012-08-27T11:33:13Z 2012-08-27T11:33:13Z 2004-04 Thesis http://hdl.handle.net/10019.1/50050 en_ZA Stellenbosch University vi, 67 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Group theory Factorization (Mathematics) Oberholzer, Ria M. On subnormal subgroups in factorized groups |
| title | On subnormal subgroups in factorized groups |
| title_full | On subnormal subgroups in factorized groups |
| title_fullStr | On subnormal subgroups in factorized groups |
| title_full_unstemmed | On subnormal subgroups in factorized groups |
| title_short | On subnormal subgroups in factorized groups |
| title_sort | on subnormal subgroups in factorized groups |
| topic | Group theory Factorization (Mathematics) |
| url | http://hdl.handle.net/10019.1/50050 |
| work_keys_str_mv | AT oberholzerriam onsubnormalsubgroupsinfactorizedgroups |