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Prikrajšanost končnih grup : delo diplomskega seminarja
ID Pezdir, Taja (Author), ID Moravec, Primož (Mentor) More about this mentor... This link opens in a new window

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Abstract
Grupo lahko definiramo s pomočjo generatorjev in relacij med njimi. Temu rečemo prezentacija grupe. Grupo želimo predstaviti s čim manjšim številom generatorjev in relacij. Prikrajšanost končno prezentirane grupe je maksimum razlike med številom generatorjev in številom relacij, ko pretečemo vse končne prezentacije dane grupe. V delu podamo asimptotični rezultat za prikrajšanost končnih grup. Pri njegovem dokazu si pomagamo s Schurovim multiplikatorjem.

Language:Slovenian
Keywords:prosta grupa, prezentacija grupe, prikrajšanost grupe, razširitev grup, Schurov multiplikator
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2023
PID:20.500.12556/RUL-150546 This link opens in a new window
UDC:512
COBISS.SI-ID:165232643 This link opens in a new window
Publication date in RUL:20.09.2023
Views:891
Downloads:27
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Secondary language

Language:English
Title:Deficiency of finite groups
Abstract:
We can define a group using generators and relations between them. This is called a group presentation. We would like to define a group with as few generators and relations as possible. The deficiency of a group is the maximum over all finite presentations for that group of the number generators minus the number of relations. We provide an asymptotic result for the deficiency of finite groups, using the Schur multiplier.

Keywords:free group, presentation of a group, deficiency of a group, group extension, the Schur multiplier

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