Podgrupe simetrične grupe S5

diplomsko delo

Branka Čakš (Author), Dušan Pagon (Mentor)

Abstract

V diplomskem delu najprej obravnavamo grupe in njihove lastnosti in le-te ponazorimo na primerih. Nato definiramo pojme direktni produkt, homomorfizem in izomorfizem, ki jih uporabimo v osrednjem delu diplome. Predstavimo tudi ciklične in diedrske grupe, ki v tretjem poglavju nastopajo kot podgrupe simetrične grupe S5. V drugem poglavju so podrobno predstavljene simetrične grupe in njihove poglavitne lastnosti s primeri. V zadnjem, tretjem delu diplome, opišemo vse podgrupe grupe S5 in izomorfizme med njimi. Razdelimo jih na maksimalne in ne maksimalne in pokažemo, da drugih podgrup S5 ne vsebuje.

Keywords

matematika;podgrupe;grupe;simetrične grupe;permutacija;cikel;množenje;izomorfizem;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[B. Čakš]
UDC:	51(043.2)
COBISS:	18245384
Views:	2875
Downloads:	308
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Subgroups of symmetric group S5
Secondary abstract:	In the diploma work, firstly, we deal with groups and their properties. The latest we present with some examples. Then we define the following concepts: direct product, homomorphism and isomorphism. We use these concepts in the central part of the diploma work as well. We also present cyclic and dihedral groups. In chapter 3, they take a role of subgroups of the symmetric group S5. In chapter 2, symmetric groups and their main properties, based on the examples, are presented. In the last part of the diploma work we describe all of the subgroups of the group S5, and the isomorphisms between them. Then we divide them to maximal and non-maximal subgroups. We also show, that there are no other subgroups in S5.
Secondary keywords:	a permutation;a cycle;a transposition;permutation multiplication;a group;a subgroup;subgroup power;a maximal subgroup;isomorphism;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VII, 43 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19160