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undergraduate thesis
Sylowljeva teorija
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2015. urn:nbn:hr:126:000637
Ostopanj, Dragana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group

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Ostopanj, D. (2015). Sylowljeva teorija (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:000637

Ostopanj, Dragana. "Sylowljeva teorija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2015. https://urn.nsk.hr/urn:nbn:hr:126:000637

Ostopanj, Dragana. "Sylowljeva teorija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2015. https://urn.nsk.hr/urn:nbn:hr:126:000637

Ostopanj, D. (2015). 'Sylowljeva teorija', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 March 2023, https://urn.nsk.hr/urn:nbn:hr:126:000637

Ostopanj D. Sylowljeva teorija [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2015 [cited 2023 March 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:000637

D. Ostopanj, "Sylowljeva teorija", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:126:000637

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Metadata
TitleSylowljeva teorija
Title (english)Sylow theory
AuthorDragana Ostopanj
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2015-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Tema ovog završnog rada je objasniti sto su to Sylowljevi teoremi, što su Sylowljeve podgrupe i koliko ih ima te koliki je njihov red. Započet ćemo definicijom Sylowljeve podgrupe, a nakon iskazivanja Sylowljevih teorema reći ćemo nesto o posljedicama istih. Zatim ćemo objasniti tranzitivno djelovanje podgrupe te tako doći do Frattinijevog teorema. Bitno pitanje u pogledu konačnih grupa je pitanje prostosti koje ćemo pojasniti u jednome od poglavlja kao i broj elemenata prostog reda. Rad ćemo završiti Schur-Zassenhausovim teoremom koji nam govori o komplementima normalnih podgrupa.
Abstract (english)
The topic of this nal paper is to explain what exactly are Sylow Theorems,what are Sylow subgroups and how many of them are there as well as which is their order. We will start with a denition of a Sylow subgroup and after state of Sylow Theorems we will say something about the consequences of such. Then, we will explain transitive action of a subgroup as well as how to reach to the Frattini Theorem. An important question with respect to nal subgroups is the question of simplycity as well as the number of elements of a prime order which will be explained in one of the upcoming chapters. This paper will be concluded with Schur-Zassenhaus Theorem which gives us an insight in complements of normal subgroups.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:000637
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of Department of Mathematics Osijek
Created on2015-11-05 09:23:53