Klasifikacija grup majhnih redov

Abstract

Keywords

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[A. Smrtnik]
UDC:	51(043.2)
COBISS:	9678409
Views:	956
Downloads:	175
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Classification of groups of small orders
Secondary abstract:	In the present BsC thesis we deal with algebraic structures, called groups. A group is a set closed under a binary operation which is associative, has an identity and in which each element has an inverse. Groups are usually studied up to group isomorphisms. Using basic results of group theory, encountered during our undergraduate studies, we classify all groups of small orders up to order 23, with the exception of groups of order 16, of course only up to isomorphism of groups. We determine how many groups of a particular order there are and name them. Furthermore, we also determine the number of elements of each possible order. We present all nonstandard groups as groups of corresponding permutations for which a corresponding multiplication table is written.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Fak. za matematiko in fiziko, Matematika in fizika
Pages:	V str., 59 f., [5] str. pril.
Type (ePrints):	thesis
Title (ePrints):	Classification of groups of small orders
Keywords (ePrints):	grupa
Keywords (ePrints, secondary language):	group
Abstract (ePrints):	V diplomskem delu obravnavamo algebrske strukture, imenovane grupe. Grupa je množica skupaj z dvočleno operacijo na njej, ki je asociativna, ima nevtralni element, poleg tega pa za vsak element obstaja ustrezni inverz. Običajno jih študiramo do izomorfizma natančno. S pomočjo osnovnih rezultatov teorije grup, ki smo jih spoznali tekom študija, klasificiramo vse grupe majhnih redov do vključno reda 23, z izjemo grup reda 16, seveda le do izomorfizma grup natančno. Določimo, koliko je vseh grup določenega reda in jih poimenujemo. Prav tako določimo število elementov vsakega možnega reda. Nestandardne grupe predstavimo tudi kot grupe ustreznih permutacij in zanje zapišemo ustrezno tabelo produktov.
Abstract (ePrints, secondary language):	In the present BsC thesis we deal with algebraic structures, called groups. A group is a set closed under a binary operation which is associative, has an identity and in which each element has an inverse. Groups are usually studied up to group isomorphisms. Using basic results of group theory, encountered during our undergraduate studies, we classify all groups of small orders up to order 23, with the exception of groups of order 16, of course only up to isomorphism of groups. We determine how many groups of a particular order there are and name them. Furthermore, we also determine the number of elements of each possible order. We present all nonstandard groups as groups of corresponding permutations for which a corresponding multiplication table is written.
Keywords (ePrints, secondary language):	group
ID:	8311508