Kratki zakoni v grupah

Knap, Jaša (author), Jezernik, Urban (mentor)

Bistvo diplomske naloge je predstaviti različne konstrukcije kratkih netrivialnih zakonov v grupah. Pri tem obravnavamo naravne družine grup, ki se pri tem pojavijo, kot so na primer nilpotentne, rešljive, enostavne in simetrične. Na koncu predstavimo, kako se iskanja zakonov lotimo z uporabo računalnika.

• Language: Slovenian
• Keywords: zakoni v grupah, proste grupe, nilpotentne grupe, rešljive grupe, enostavne grupe, simetrične grupe, Cayleyjevi grafi, GAP
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-161818
• Publication date in RUL: 14.09.2024

Secondary language

• Language: English
• Title: Short Group Laws

Abstract

The purpose of this thesis is to present various constructions of short group laws. In order to do so, we examine the properties of nilpotent, solvable, simple, and symmetric groups. The thesis is concluded by illustrating how computational methods can be used to discover group laws.

• Keywords: group laws, free groups, nilpotent groups, solvable groups, simple groups, symmetric groups, Cayley graphs, GAP