undergraduate thesis
Sylow theory

Dragana Ostopanj (2015)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
Metadata
TitleSylowljeva teorija
AuthorDragana Ostopanj
Mentor(s)Ivan Matić (thesis advisor)
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.
KeywordsSylow Theorems Sylow subgroups number of subgroups Frattini The- orem groups of a prime order elements of a prime order Schur-Zassenhaus Theorem
Parallel title (English)Sylow theory
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Algebra
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2015-09-30
Parallel 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.
Parallel keywords (Croatian)Sylowljevi teoremi Sylowljeve podgrupe broj podgrupa Frattinijev teorem grupe prostog reda elementi prostog reda Schur-Zassenhausov teorem
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:000637
CommitterMirna Šušak Lukačević