Proširenja grupa

master's thesis

• Author: Helena Schill
• Mentor: Ozren Perše (mentor)
• Committee member: Ozren Perše (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Nikola Sarapa (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-23, 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: proširenje grupe; semidirektni produkt; kohomologija; Schreireov teorem; Schur-Zassenhausova lema
• Keywords (english): group extensions; semidirect product; cohomology; Schreir’s theorem; Schur-Zassenhaus lemma
• Language: croatian
• URN:NBN: urn:nbn:hr:217:527890
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-06 14:05:42