NEKOMUTITATIVNE GRUPE I SIMPLICIJALNI KOMPLEKSI

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NEKOMUTITATIVNE GRUPE I SIMPLICIJALNI KOMPLEKSI

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dc.contributor.advisor Petrović, Zoran
dc.contributor.author Kostić, Aleksandra
dc.date.accessioned 2021-01-18T16:29:20Z
dc.date.available 2021-01-18T16:29:20Z
dc.date.issued 2021
dc.identifier.uri http://hdl.handle.net/123456789/5096
dc.description.abstract This dissertation examines simplicial complexes associated with cyclotomic po-lynomials and irreducible characters of finite solvable groups. In the process of analysis ofthe associated objects special attention is paid to the noncommutativity of the examinedstructures.A collection of simplicial complexes can be associated to an algebraic object such as acyclotomic polynomial. In most cases, the homotopy type of associated simplicial complexesgives us complete information about the coefficients of the cyclotomic polynomial. The onlyexceptions are cyclotomic polynomials whose degree is a product of three different primenumbers and this case is the focus of research in this doctoral dissertation. When it ispossible, the homotopy type of a simplicial complex associated with the polynomialΦpqr(x),wherep,qandrare different prime numbers, is determined by using the discrete Morsetheory. However, in special cases, the simplicial complexes associated with the polynomialΦpqr(x)have a noncommutative fundamental group, thus providing a new noncommutativeinvariant of this type of polynomial. Complex presentations that appear as presentations ofthe fundamental groups of associated simplicial complexes are analyzed using Fox’s calculus.This thesis also focus on the study of simplicial complexes associated to a set of irreduciblecharacters of a finite solvable group. Two types of simplicial complexes are attached to aset of irreducible characters of a finite solvable group — character degree complex and primedivisor complex. The examination of the fundamental group of these types of simplicial com-plexes provides better understanding of the structure of the irreducible characters of finitesolvable groups. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2021-01-18T16:29:20Z No. of bitstreams: 1 Teza-Aleksandra_Kostic.pdf: 1009044 bytes, checksum: 32bfc6e30fd5415428ffc4a4211047bb (MD5) en
dc.description.provenance Made available in DSpace on 2021-01-18T16:29:20Z (GMT). No. of bitstreams: 1 Teza-Aleksandra_Kostic.pdf: 1009044 bytes, checksum: 32bfc6e30fd5415428ffc4a4211047bb (MD5) Previous issue date: 2021 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title NEKOMUTITATIVNE GRUPE I SIMPLICIJALNI KOMPLEKSI en_US
mf.author.birth-date 1989-05-12
mf.author.birth-place Loznica en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords implicial complexes, fundamental group, noncommutativity, homotopy type,cyclotomic polynomials, irreducible characters, solvable groups, Fox calculus, discrete Morsetheory en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Ikodinović, Nebojša
mf.contributor.committee Đanković, Goran
mf.contributor.committee Baralić, Đorđe
mf.university.faculty Mathematical faculty en_US
mf.document.references 45 en_US
mf.document.pages 114 en_US
mf.document.location Belgrade en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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