Policiklična domneva in izmuzljive permutacijske grupe

magistrsko delo

Matevž Miščič (Author), Primož Potočnik (Mentor)

Abstract

V delu obravnavamo izmuzljive permutacijske grupe. Spoznamo veliko primerov takšnih grup, med drugim kot pomemben primer skonstruiramo Mathieujevo grupo $M_{11}$. Opišemo znane konstrukcije izmuzljivih grup in se ukvarjamo z možnimi stopnjami izmuzljivih grup. Klasificiramo vse primitivne izmuzljive grupe. Predstavimo policiklično domnevo in pokažemo, da nobena od opisanih konstrukcij izmuzljivih grup ne privede do protiprimera za to domnevo. Pokažemo tudi, da nobena tranzitivna grupa avtomorfizmov vozliščno tranzitivnega grafa valence $3$ ali $4$ ni izmuzljiva. Predstavimo tudi rezultate o največjem redu semiregularnega avtomorfizma kubičnega vozliščno tranzitivnega grafa.

Keywords

permutacijske grupe;policiklična domneva;izmuzljive grupe;vozliščno tranzitiven graf;semiregularen automorfizem;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Miščič]
UDC:	512.54
COBISS:	207219459
Views:	108
Downloads:	39
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Polycirculant conjecture and elusive permutation groups
Secondary abstract:	We consider elusive permutation groups. Many examples of such groups are introduced, including the Mathieu group $M_{11}$ as an important example. We describe the known constructions of elusive groups and discuss the possible degrees of elusive groups. We classify all primitive elusive groups. We introduce the polycirculant conjecture and show that none of the described constructions of elusive groups leads to a counterexample for this conjecture. We also show that no transitive group of automorphisms of a vertex transitive graph of valency $3$ or $4$ is elusive. We also present some results on the highest order semiregular automorphism of a cubic vertex transitive graph.
Secondary keywords:	permutation groups;polycircuant conjecture;elusive groups;vertex transitive graph;semiregular automorphism;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages:	X, 84 str.
ID:	25031390