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master's thesis
Normalne podgrupe i kvocijentne grupe
2023. urn:nbn:hr:126:516704
Brzić, Lucija
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Cite this document

Brzić, L. (2023). Normalne podgrupe i kvocijentne grupe (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:516704

Brzić, Lucija. "Normalne podgrupe i kvocijentne grupe." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:516704

Brzić, Lucija. "Normalne podgrupe i kvocijentne grupe." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:516704

Brzić, L. (2023). 'Normalne podgrupe i kvocijentne grupe', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 12 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:516704

Brzić L. Normalne podgrupe i kvocijentne grupe [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 November 12] Available at: https://urn.nsk.hr/urn:nbn:hr:126:516704

L. Brzić, "Normalne podgrupe i kvocijentne grupe", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:516704

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Metadata
TitleNormalne podgrupe i kvocijentne grupe
Title (english)Normal Subgroups And Quotient Groups
AuthorLucija Brzić
MentorIvan Matić (mentor)
Committee memberIvan Soldo (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberLjiljana Primorac Gajčić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-10-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu definirali smo pojmove grupoida, monoida, grupe i podgrupe te naveli važne tvrdnje vezane uz njih. Upoznali smo se s pojmom Abelove grupe, pokazali kako odrediti podgrupu grupe i definirali pojmove homomorfizma, monomorfizma, epimorfizma i izomorfizma grupe. Definirali smo normalne podgrupe, naveli primjere i važne teoreme, a najvažniji među njima je Lagrangeov teorem. Uz to smo uveli i objasnili pojmove centralizatora i normalizatora skupa u grupi te centra grupe. Na kraju smo rekli nešto o kvocijentnim grupama, komutativnom dijagramu, egzaktnom nizu te o Prvom, Drugom i Trećem teoremu o izomorfizmu.
Abstract (english)
In this thesis, we have defined the concepts of groupoid, monoid, group and subgroup and stated important claims related to them. We were acquainted with the concept of Abelian group, showed how to determine a subgroup of a group and defined the concepts of group homomorphism, monomorphism, epimorphism and isomorphism. We have defined normal subgroups, given examples and important theorems, the most important of which is Lagrange’s theorem. In addition, we introduced and explained the concepts of the centralizer and normalizer of a set in a group and center of a group. Finally, we said something about quotient groups, commutative diagram, exact sequence and about the First, Second and Third isomorphism theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:516704
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-11-08 12:28:12