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master's thesis
Proširenja grupa
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:527890
Schill, Helena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Schill, H. (2015). Proširenja grupa (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:527890

Schill, Helena. "Proširenja grupa." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:527890

Schill, Helena. "Proširenja grupa." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:527890

Schill, H. (2015). 'Proširenja grupa', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:527890

Schill H. Proširenja grupa [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:527890

H. Schill, "Proširenja grupa", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:527890

Metadata
TitleProširenja grupa
AuthorHelena Schill
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavamo pojam proširenja grupe. Dokazujemo važan rezultat o bijekciji između proširenja i grupe kohomologije. U prvom poglavlju ponavljamo osnovne definicije i rezultate iz algebarskih struktura. U drugom poglavlju uvodimo pojam semidirektnog produkta i njegova svojstva. Treće poglavlje se bavi generalnim proširenjima i kohomologijom. Uvodimo pojmove kociklusa koristeći pojam podizanja. U ovom poglavlju dolazimo do najbitnijih rezultata rada, Schreireovog teorema koji koristi kocikluse u rješavanju problema proširenja te kao njegovu posljedicu, Schur-Zassenhausovu lemu.
Abstract (english)
In this diploma thesis we study group extensions. We prove important result about bijection between extensions and group cohomology. In first chapter we recall basic definitions and results from algebraic structures. In second chapter we introduce the idea of semidirect product and its properties. The third chapter is about general extensions and cohomology. We introduce the concept of cocycle using the definition of lifting. In this chapter we prove the most important results of the thesis, Schreir’s theorem which uses cocycle to solve the extension problem and Schur-Zassenhaus lemma which is it’s consequence.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:527890
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-06 14:05:42