Delovanja grup in bloki neprimitivnosti : diplomsko delo

Krejić, Dejan (author), Šparl, Primož (mentor)

Diplomsko delo spada na področje teorije grup. V njem obravnavamo delovanja grup, največ pozornosti pa posvetimo raziskovanju blokov neprimitivnosti in njihovih lastnosti. Gre za pomemben koncept v teoriji permutacijskih grup, saj obstoj tako imenovanega sistema blokov neprimitivnosti za dano delovanje pogosto omogoča, da obravnavo danega delovanja zreduciramo na delovanje na precej manjši množici, s čimer postane bolj obvladljivo. V diplomskem delu zberemo temeljna znanja, ki so potrebna za razumevanje osrednje teme. Spoznamo delovanja grup ter z njimi povezane lastnosti in rezultate, predstavimo pa tudi nekaj konkretnih primerov. Vpeljemo pojem bloka neprimitivnosti, raziščemo kriterij za njihov obstoj in jih predstavimo na nekaj zgledih. Bloke neprimitivnosti povežemo s pojmom neprimitivnega delovanja in podamo potrebne ter zadostne pogoje za opredelitev primitivnosti in neprimitivnosti delovanja. Ogledamo si konkretne primere primitivnih in neprimitivnih delovanj grup. Raziščemo povezavo med netranzitivnimi edinkami in bloki neprimitivnosti.

• Language: Slovenian
• Keywords: teorije grup, blok neprimitivnosti, delovanje grupe, primitivnost, sistem blokov neprimitivnosti
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [D. Krejić]
• Year: 2015
• Number of pages: 29 str.
• PID: 20.500.12556/RUL-72689
• UDC: 512.5(043.2)
• COBISS.SI-ID: 10714441
• Publication date in RUL: 29.09.2015

KREJIĆ, Dejan, 2015, Delovanja grup in bloki neprimitivnosti : diplomsko delo [online]. Bachelor’s thesis. D. Krejić. [Accessed 8 April 2025]. Retrieved from: http://pefprints.pef.uni-lj.si/id/eprint/3069

Secondary language

• Language: English
• Title: Group actions and blocks of imprimitivity

Abstract

This BSc thesis deals with certain topics from group theory. We investigate group actions and in particular devote most of our attention to the research of blocks of imprimitivity and their characteristics. This is a very important concept in the theory of permutation groups, since the existence of the so-called imprimitivity block system for a given action, often enables us to reduce the action to a much smaller set, which makes it more manageable. In the thesis, we collect the basic notions and results that are necessary for the understanding of the central theme. We review some basic facts about group actions and their properties and present some examples. We introduce the concept of a block of imprimitivity, we explore the criterion for their existence and we give some examples of them. We link the concept of blocks of imprimitivity with the concept of an imprimitive action and present necessary and sufficient conditions for the action to be primitive or imprimitive. We present examples of primitive and imprimitive group actions and explore the connection between intransitive normal subgroups and blocks of imprimitivity.

• Keywords: block of imprimitivity