Normal Subgroups And Quotient Groups

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.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