On the theory and examples of group extensions.

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dc.contributor.advisor Moori, Jamshid.
dc.creator Rodrigues, Bernardo Gabriel.
dc.date.accessioned 2012-07-17T13:34:42Z
dc.date.available 2012-07-17T13:34:42Z
dc.date.created 1999
dc.date.issued 1999
dc.identifier.uri http://hdl.handle.net/10413/5971
dc.description Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1999. en
dc.description.abstract The work described in this dissertation was largely motivated by the aim of producing a survey on the theory of group extensions. From the broad scope of the theory of group extensions we single out two aspects to discuss, namely the study of the split and the non-split cases and give examples of both. A great part of this dissertation is dedicated to the study of split extensions. After setting the background theory for the study of the split extensions we proceed in exploring the ramifications of this concept within the development of the group structure and consequently investigate well known products which are its derived namely the holomorph, and the wreath product. The theory of group presentations provides in principle the necessary tools that permit the description of a group by means of its generators and relators. Through this knowledge we give presentations for the groups of order pq,p2q and p3. Subsequently using a classical result of Gaschutz we investigate the split extensions of non-abelian groups in which the normal subgroup is either a non-abelian normal nilpotent group or a non-abelian normal solvable group. We also study other cases of split extensions such as the affine subgroups of the general linear and the symplectic groups. It is expected that some of the results obtained will provide a theoretical algorithm to describe these affine subgroups. A particular case of the non-split extensions is discussed as the Frattini extensions. In fact a simplest example of a Frattini extension is a non-split extension in which the kernel of an epimorphism e is an irreducible G-module. en
dc.language.iso en_ZA en
dc.subject Group extensions (Mathematics) en
dc.subject Group theory. en
dc.subject Groups, Theory of. en
dc.subject Theses--Mathematics. en
dc.title On the theory and examples of group extensions. en
dc.type Thesis en

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