SubjectsSubjects(version: 945)
Course, academic year 2023/2024
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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
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:
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 > Volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG017
Interchangeability : NALG017
Is interchangeable with: NALG017
In complex pre-requisite: NMAG349, NMAG351
Annotation -
Last update: G_M (15.05.2012)
A recommended course on group theory for specialization Mathematical Structures within General Mathematics.
Course completion requirements -
Last update: doc. RNDr. David Stanovský, Ph.D. (21.09.2023)

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

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


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


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.

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

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.

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

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.

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