Semren, Matea (2014) NielsenSchreierov teorem. Diploma thesis, Faculty of Science > Department of Mathematics.

PDF
Language: Croatian Download (229kB)  Preview 
Abstract
In this thesis we prove one of the fundamental results about free groups. That is the NielsenSchreier theorem, which says that every subgroup of free group is also free group. First, we define a group, a subgroup, a generated subgroup, a normal subgroup and quotient groups which allows us to construct a new group from given group. We will also define a homomorphism between groups, and specially an isomorphism, and prove the three isomorphism theorems. In second part, first, we define a direct sum, which allows us to define a free abelian group and its basis. The characterisation of free abelian groups is our motivation for more general definition of free groups. We prove existence of nonabelian free group by constructing it from some nonempty set, which is a basis for that free group. Then, we define a transversal, and specially Schreier transversal, which allows us to define a basis for a subgroup of free group. In the end, we give some applications of the NielsenSchreier theorem.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Perše, Ozren 
Date:  2014 
Number of Pages:  33 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  09 Jul 2015 12:38 
Last Modified:  09 Jul 2015 12:38 
URI:  http://digre.pmf.unizg.hr/id/eprint/4106 
Actions (login required)
View Item 