Slobodne grupe i prezentacije

Čukec, Petra (2015) Slobodne grupe i prezentacije. Diploma thesis, Faculty of Science > Department of Mathematics.

Language: Croatian

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Theme of this thesis are free groups and presentations. In introduction we defined basic terms related to groups and mappings between them. We defined the term category and showed several examples, the most important one being the category of groups. We defined what a free object in a concrete category is. Especially, we defined a free group as a free object on set X in category of groups. After that, we defined the terms: word, the inverse of a nonempty word, a subword and a reduced word and we have shown that set of all reduced words with operations juxtaposition and elementary cancellation is equivalent to the term free group with basis X. We mentioned the most important results related to free Abelian groups needed for this thesis. Previously defined free Abelian groups and commutator subgroups are connected with free groups and their rank is defined. In the last chapter we showed that every group has a presentation and mentioned several examples of presentations such as a presentation of the group of quaternions and dihedral group.

Item Type: Thesis (Diploma thesis)
Supervisor: Adamović, Dražen
Date: 2015
Number of Pages: 46
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 07 Oct 2015 09:35
Last Modified: 07 Oct 2015 09:35

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