Rešljive grupe : diplomsko delo

Kos, Blaž (author), Šparl, Primož (mentor)

V diplomskem delu obravnavamo pojem rešljive grupe. Le-te se izkažejo za zelo pomemben koncept znotraj teorije grup. Pred samo vpeljavo pojma rešljive grupe najprej ponovimo osnovne definicije in rezultate teorije grup, ki so potrebni za razumevanje diplomskega dela. Nato vpeljemo pojem (pod)normalne vrste in ga ilustriramo na primerih. Prav tako definiramo pojma kompozicijske in komutatorske vrste ter ju ilustriramo na primerih. Nazadnje vpeljemo še pojem rešljive grupe. Poiščemo kriterij, kdaj je dana končna grupa rešljiva. Podamo primere rešljivih in nerešljivih grup in predstavimo še nekaj rezultatov, povezanih z rešljivimi grupami.

• Language: Slovenian
• Keywords: (pod)normalna vrsta, kompozicijska vrsta, komutatorska vrsta
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [B. Kos]
• Year: 2015
• Number of pages: 25 str.
• PID: 20.500.12556/RUL-72613
• UDC: 51(043.2)
• COBISS.SI-ID: 10697033
• Publication date in RUL: 29.09.2015

KOS, Blaž, 2015, Rešljive grupe : diplomsko delo [online]. Bachelor’s thesis. B. Kos. [Accessed 8 April 2025]. Retrieved from: http://pefprints.pef.uni-lj.si/id/eprint/3035

Secondary language

• Language: English
• Title: Solvable groups

Abstract

In this BSc thesis we consider the concept of solvable groups. It turns out that this concept is one of the most important ones in group theory, since these groups in a sense correspond to groups that can be constructed from cyclic groups of prime order. Before introducing the concept of solvable groups we make a short review of some notions and results in group theory. We then define the concept of (sub)normal series and illustrate it with a few examples. We also define the concepts of composition series and commutator series. We then finally introduce the concept of solvable groups. We present a criterion of when a finite group is solvable. We give examples of solvable and nonsolvable groups and present some other results related to the concept of solvable groups.

• Keywords: mathematics