p-grupe

magistrsko delo

Urška Bezjak (Author), Mateja Grašič (Mentor)

Abstract

Cilj magistrskega dela je spoznati p-grupe in z njimi povezane izreke Sylowa. Najprej obravnavamo osnovne pojme teorije grup, ki jih potrebujemo za razumevanje magistrskega dela. Spoznamo enačbo razreda in proučimo morfizme grup ter vpeljemo direktni produkt grup. Največjo pozornost namenimo p-grupam, izrekom Sylowa in njihovi uporabi v klasifikaciji grup majhnih redov. Obravnavamo končne p-grupe in njihove najpomembnejše lastnosti, nekaj časa pa namenimo tudi neskončnim p-grupam, ki jih spoznavamo na primeru Prüferjevih grup.

Keywords

magistrska dela;p-grupe;izreki Sylowa;enačba razreda;izomorfizem grup;direktni produkt grup;grupe majhnih redov;Prüferjeve grupe;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[U. Bezjak]
UDC:	512.54(043.2)
COBISS:	23323400
Views:	895
Downloads:	166
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	p-groups
Secondary abstract:	The aim of the master thesis is to present p-groups and the related Sylow theorems. In our master thesis we examine basic concepts of group theory which are needed for understanding the concepts that follow. We define the class equation, study group morphisms and introduce the direct product of groups. We pay the greatest attention to p-groups, the Sylow theorems and their use in the classification of groups of small orders. We examine finite p-groups and their most important properties. We also devote some of the time to infinite p-groups which we get to know on the example of Prüfer groups.
Secondary keywords:	master theses;p-groups;Sylow theorems;class equation;group isomorphism;direct product of groups;groups of small orders;Prüfer groups;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	XI, 38 f.
ID:	10859675