Poldirektni produkt grup

diplomsko delo

Lucija Žnidarič (Author), Primož Šparl (Mentor)

Abstract

V diplomskem delu obravnavamo konstrukcijo grup, imenovano poldirektni produkt grup. Gre za posplošitev direktnega produkta, ki omogoča konstrukcije precej večjega nabora grup. Poiščemo kriterij, kdaj je dana grupa poldirektni produkt grup, in prikažemo razliko med direktnim in poldirektnim produktom. Ogledamo si konkretne zglede poldirektnih produktov grup, osredotočimo se predvsem na poldirektne produkte cikličnih grup. Pokažemo tudi, da se poldirektni produkti pojavljajo kot grupe simetrij kombinatoričnih objektov, kot so grafi in da je lahko dana grupa izomorfna večim poldirektnim produktom.

Keywords

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Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[L: Žnidarič]
UDC:	512(043.2)
COBISS:	10255689
Views:	877
Downloads:	155
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Semidirect product of groups
Secondary abstract:	In this BSc thesis we consider a construction of groups called semidirect product, which is a generalization of direct products. Semidirect products provide a much larger collection of groups than direct products. We find a criterion, which enables us to determine whether a group is isomorphic to a semidirect product and discuss the difference between direct and semidirect products. We construct various examples of semidirect products and in particular semidirect products of cyclic groups. We exemplify that semidirect group products also take a role as symmetry groups of combinatorial objects such as graphs.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in računalništvo
Pages:	34 str.
ID:	8708287