Predstavitve simetričnih in alternirajočih grup

magistrsko delo

Dijana Slemenšek (Author), Dušan Pagon (Mentor)

Abstract

V magistrskem delu so v prvem delu obravnavane osnovne lastnosti simetričnih in alternirajočih grup. V drugem poglavju je podrobnejši pregled osnovne predstavitve grup Sn dolžine O(n), v nadaljnjih dveh poglavjih pa je predstavljena celotna konstrukcija predstavitev grup Sm+n in Smn iz grup Sm ter Sn. Zaradi obsežne dolžine predstavitev simetričnih grup so predstavljeni tudi načini zmanjšanja števila povezav in kratke predstavitve teh grup. Za konec so podrobneje opisane tudi alternirajoče grupe in prikazani nekateri primeri kratkih predstavitev za primere simetričnih grup nizkih redov.

Keywords

simetrične grupe;alternirajoče grupe;generatorji;povezave;magistrska dela;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[D. Slemenšek]
UDC:	512.54(043.2)
COBISS:	20803592
Views:	1289
Downloads:	183
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Presentations of symmetric and alternating groups
Secondary abstract:	In the master's thesis we first provide all necessary basic features of the symmetric and alternating groups. Further on, we take a closer look at a basic presentations for these groups with length O(n). In next couple of chapters we present an entire construction of the presentations for groups Sm+n and Smn starting from groups Sm and Sn. Due to quite long standard presentation of symmetric group we show how to shorten the number of relations and present those groups with a short presentation. As a conclusion we also present the alternating groups in more details and give some concrete examples of short presentations for symmetrical groups of small degrees.
Secondary keywords:	symmetric groups;alternating groups;generators;relations;thesis;
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:	VIII, 37 f.
ID:	8729904