Klasifikacija grup majhnih redov

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2013
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[A. Smrtnik]
UDK:	51(043.2)
COBISS:	9678409
Št. ogledov:	956
Št. prenosov:	175
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Classification of groups of small orders
Sekundarni povzetek:	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.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Fak. za matematiko in fiziko, Matematika in fizika
Strani:	V str., 59 f., [5] str. pril.
Vrsta dela (ePrints):	thesis
Naslov (ePrints):	Classification of groups of small orders
Ključne besede (ePrints):	grupa
Ključne besede (ePrints, sekundarni jezik):	group
Povzetek (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.
Povzetek (ePrints, sekundarni jezik):	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.
Ključne besede (ePrints, sekundarni jezik):	group
ID:	8311508