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dc.contributor.advisorMeyer, J. H.
dc.contributor.authorDe Klerk, Ben-Eben
dc.date.accessioned2017-08-07T07:38:17Z
dc.date.available2017-08-07T07:38:17Z
dc.date.issued2016-09
dc.identifier.urihttp://hdl.handle.net/11660/6521
dc.description.abstractEnglish: Given a set S, and any selfmap ƒ: S→S, the functional graph associated with ƒ can be described as a graph with vertex set S and directed edge set E = {(u; v) ϵ S2 : ƒ (u) = v}. A classification of all functional graphs induced by lattice endomorphisms has recently been done by J. Szigeti ([12]). In this dissertation, we aim to achieve a similar type of classi_cation with respect to functional graphs induced by endomorphisms on certain abelian groups. A method for finding all functional graphs that can be induced by endomorphisms of a group has been developed for all groups of the form Znp with p any prime, n ϵ N, and Zn for any n ϵ N, as well as all cyclic groups. A deep connection between the functional graphs corresponding to group endomorphisms and the minimal polynomial of the matrix representation of the group endomorphism has been found.en_ZA
dc.description.abstractAfrikaans: Gegewe 'n versameling S, en enige selfafbeelding ƒ: S →S, kan die funksionele grafiek geassosieer met ƒ beskryf word as die grafiek met nodus versameling S en gerigte randversameling E = {(u; v) ϵ S2 : ƒ (u) = v}. 'n Klassifikasie van alle funksionele grafi eke wat deur tralie endomor fismes geinduseer word, was onlangs deur J. Szigeti gedoen ([12]). In hierdie verhandeling beoog ons om 'n soortgelyke tipe klassi fikasie te bekom met betrekking tot die funksionele gra fieke eke wat deur endomor fismes van sekere abelse groepe geinduseer word. 'n Metode vir die bepaling van alle funksionele grafieke wat geinduseer word deur endomorsmes van 'n groep is ontwikkel vir alle groepe van die vorm Znp met p enige priem, n ϵ N, en Zn vir enige n ϵ N, sowel as alle sikliese groepe. 'n Belangrike verband tussen die funksionele gra fieke wat ooreenstem met groep endomor smes en die minimale polinoom van die matriks voorstelling van die endomor fisme gevind.af
dc.language.isoenen_ZA
dc.publisherUniversity of the Free Stateen_ZA
dc.subjectAbelian Groupen_ZA
dc.subjectAutomorphismen_ZA
dc.subjectEndomorphismen_ZA
dc.subjectConjugacy classesen_ZA
dc.subjectFunctional graphen_ZA
dc.subjectTreeen_ZA
dc.subjectFinite fielden_ZA
dc.subjectCyclotomic polynomialen_ZA
dc.subjectMinimal polynomialen_ZA
dc.subjectThesis (Ph.D. (Mathematics and Applied Mathematics))--University of the Free State, 2016en_ZA
dc.titleA structural approach to the endomorphisms of certain abelian groupsen_ZA
dc.typeThesisen_ZA
dc.rights.holderUniversity of the Free Stateen_ZA


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