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En lösning till ordproblemet för Coxetergrupper
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
A solution to the word problem for Coxeter groups (English)
Abstract [sv]

I denna rapport undersöks en abstrakt representation av reflektionsgrupper kallade Coxetergrupper. Inledningsvis ges en introduktion till gruppteori. Sedan beskrivs ett koncept som kallas ordproblemet. Efter det presenteras ett sätt att definiera grupper utifrån en mängd generatorer och relationer. Denna teori används för att definiera Coxetergrupper och ge en klassificering av de ändliga Coxetergrupperna som H.S.M. Coxeter presenterade 1935. Avslutningsvis presenteras lösningen till ordproblemet i Coxetergrupper, och några tillämpningar av teorin diskuteras.

Abstract [en]

In this report, we study an abstract representation of reflection groups called Coxeter groups. Firstly, we introduce some important aspects of group theory. Next, we describe a concept called the word problem. Then, a way of defining groups given a set of generators and relations is presented. This theory is used to define the Coxeter groups, followed by a complete classification of the finite Coxeter groups as presented by H.S.M. Coxeter in 1935. Finally, we present a solution to the word problem for Coxeter groups and discuss some applications.

 

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:116
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254706OAI: oai:DiVA.org:kth-254706DiVA, id: diva2:1334807
Supervisors
Examiners
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf