Frizne grupe : delo diplomskega seminarja

Janičijevič, Aleksander (author), Vavpetič, Aleš (mentor)

Diplomska naloga se ukvarja s friznimi grupami. Na Evklidski ravnini, opremljeni z Evklidsko metriko, definira množico vseh izometrij, nato pa obravnava najpreprostejše primere le-teh (to so translacija, rotacija in zrcaljenje). S pomočjo kompozitumov translacij, rotacij in zrcaljenj nato predstavi tudi vse frizne grupe. Cilj diplomske naloge je opisati (klasificirati) frizne grupe ter dokazati, da jih je, geometrijsko gledano, natanko sedem.

• Language: Slovenian
• Keywords: metrični prostor, izometrija, grupa, podgrupa, podgrupa edinka, prezentacija grupe, translacija, rotacija, zrcaljenje, zrcalni zdrs, fiksna točka, orientacija, diskretna podgrupa, translacijska podgrupa, frizna grupa
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-134448
• UDC: 512
• COBISS.SI-ID: 94713603
• Publication date in RUL: 15.01.2022

Secondary language

• Language: English
• Title: Frieze groups

Abstract

The diploma thesis deals with frieze groups. In the Euclidean space under the Euclidean metric, it defines the set of all isometries and then deals with the most basic cases of such isometries (them being translation, rotation and reflection). Using compositions of translations, rotations and reflections, it then presents all the frieze groups. The goal of the diploma thesis is to classify frieze groups and prove that there are exactly seven geometrically different types of them.

• Keywords: metric space, isometry, group, subgroup, normal subgroup, presentation of a group, translation, rotation, reflection, glide reflection, fixed point, orientation, discrete subgroup, translation subgroup, frieze group