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On subnormal subgroups in factorized groupsOberholzer, Ria M 04 1900 (has links)
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.
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The maximal subgroups of the sporadic groups Th, Fiâ†2â†4 and Fi'â†2â†4 and other topicsLinton, Stephen Alexander January 1989 (has links)
No description available.
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83 |
Extended algebras in conformal field theoryWatts, Gerard Marcel Tannerie January 1990 (has links)
No description available.
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84 |
The subgroup separability of some amalgamated free productsNiblo, G. A. January 1988 (has links)
No description available.
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85 |
Combinatorial formulas, invariants and structures associated with primitive permutation representations of PSL(2,q) and PGL(2,q)Kamuti, Ireri Nthiga January 1992 (has links)
No description available.
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86 |
Topics in products of nilpotent groupsSmith, Jeremy Francis January 1998 (has links)
No description available.
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87 |
A class of A-groupsMakarfi, U. M. January 1985 (has links)
No description available.
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88 |
Algorithms for computing in finite groupsBamblett, Jane Carswell January 1994 (has links)
No description available.
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89 |
Ends of permutation groups and some centrality properties of permutational wreath productsCernes, John January 1996 (has links)
No description available.
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90 |
Some topics in group theoryCartwright, M. January 1984 (has links)
No description available.
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