Introduction to Group Theory - NMAG337
Title: Úvod do teorie grup
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/grupy.htm
Guarantor: doc. RNDr. David Stanovský, Ph.D.
Class: M Bc. MMIT
M Bc. MMIT > Doporučené volitelné
M Bc. OM
M Bc. OM > Zaměření MSTR
M Bc. OM > Povinně volitelné
M Mgr. MMIB
M Mgr. MMIB > Volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG017
Interchangeability : NALG017
Is interchangeable with: NALG017
In complex pre-requisite: NMAG349, NMAG351
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Annotation -
A recommended course on group theory for specialization Mathematical Structures within General Mathematics.
Last update: G_M (15.05.2012)
Course completion requirements -

Credit will be awarded for succesfully solving several homework sets (see web for details).

Last update: Stanovský David, doc. RNDr., Ph.D. (21.09.2023)
Literature -

primary:

Joseph J. Rotman: An Introduction to the Theory of Groups, Springer, New York, 1995.

secondary:

Aleš Drápal: Teorie grup : základní aspekty, Karolinum, Praha, 2000.

Derek J.S. Robinson: A Course in the Theory of Groups, Springer, New York, 1982.

M. Hall: The Theory of Groups, Macmillan Company, New York, 1959.

I.Martin: Isaacs, Finite group theory, American Mathematical Society, Providence, 2008.

L. Procházka, L. Bican, T. Kepka, P. Němec: Algebra, Academia, Praha, 1990.

Last update: Stanovský David, doc. RNDr., Ph.D. (21.09.2023)
Requirements to the exam -

Students have to pass final written exam. The requirements for the exam correspond to what has been done during lectures and practicals. For details see the website.

Last update: Stanovský David, doc. RNDr., Ph.D. (21.09.2023)
Syllabus -

1. Basic structural features (subgroups, homomorphisms, products)

2. Group actions on a set, on itself.

4. The structure of finite groups (class equation, p-groups, Sylow theorems)

5. Subnormal series (Zassenhaus lemma, Jordan-Holder theorem, solvability, nilpotence)

6. Abelian groups - free abelian groups, finitely generated abelian groups

7. Free groups, Nielsen-Schreier theorem.

Last update: Stanovský David, doc. RNDr., Ph.D. (21.09.2023)