Poldirektni produkt grup : diplomsko delo

Žnidarič, Lucija (author), Šparl, Primož (mentor)

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.

• Language: Slovenian
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [L: Žnidarič]
• Year: 2014
• Number of pages: 34 str.
• PID: 20.500.12556/RUL-69217
• UDC: 512(043.2)
• COBISS.SI-ID: 10255689
• Publication date in RUL: 10.07.2015

Secondary language

• Language: English
• Title: Semidirect product of groups

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.