Growth in finite groups and the Graph Isomorphism Problem

Dona, Daniele

dc.contributor.advisor	Helfgott, Harald Andrés Prof. Dr.
dc.contributor.author	Dona, Daniele
dc.date.accessioned	2020-08-19T12:01:33Z
dc.date.available	2020-08-19T12:01:33Z
dc.date.issued	2020-08-19
dc.identifier.uri	http://hdl.handle.net/21.11130/00-1735-0000-0005-145F-B
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-8163
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc	510	de
dc.title	Growth in finite groups and the Graph Isomorphism Problem	de
dc.type	doctoralThesis	de
dc.contributor.referee	Helfgott, Harald Andrés Prof. Dr.
dc.date.examination	2020-07-17
dc.description.abstracteng	The present thesis embraces two major areas of mathematics, namely group theory (especially growth in finite groups) and graph theory (especially the graph isomorphism problem). Several results are presented coming from both areas: on one side, we show that the dependence of the diameter of a product of finite simple groups on the diameter of its factors is linear, and we extend the analysis of sets of small growth in the affine group over a prime field to the same group over general finite fields; on the other, we show a dependence of the number of iterations of the Weisfeiler-Leman algorithm over Schreier and Cayley graphs on the diameter of such graphs. Finally, analyzing Babai's algorithm for solving the graph isomorphism problem, we pave a possible way towards a proof of a diameter bound for the alternating group that does not rely on the classification of finite simple groups.	de
dc.contributor.coReferee	Bartholdi, Laurent Prof. Dr.
dc.subject.eng	Growth in groups	de
dc.subject.eng	Graph Isomorphism Problem	de
dc.subject.eng	Diameter	de
dc.subject.eng	CFSG	de
dc.subject.eng	Weisfeiler-Leman	de
dc.subject.eng	Affine group	de
dc.subject.eng	Product of simple groups	de
dc.subject.eng	Schreier graphs	de
dc.subject.eng	Alternating group	de
dc.identifier.urn	urn:nbn:de:gbv:7-21.11130/00-1735-0000-0005-145F-B-6
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematik (PPN61756535X)	de
dc.identifier.ppn	1727500040

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

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