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Introduction to Finite Groups Theory - NALG052

Title:	Úvod do teorie konečných grup
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2011
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/0, --- [HT] summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Aleš Drápal, CSc., DSc.
Class:	Algebra v informatice Algebra v přírodních vědách DS, algebra, teorie čísel a matematická logika
Classification:	Mathematics > Algebra
Pre-requisite :	NALG017

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Annotation -

Abstract representation, cocycles and coboundaries, basic splitting theorems, Hall subgroups, Frattini subgroup, extraspecial groups, generalized Fitting subgroup. The subject can be taught in English.

Last update: T_KA (03.05.2004)

Literature - Czech

1. M. Aschbacher, Finite group theory, Cambridge University Press, 1986, 1988, 1993

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

3. B. Huppert, Endliche Gruppen, Springer-Verlag, 1971

4. D.J.S. Robinson, A Course in the Theory of Groups, Springer-Verlag, 1982

5. J.J. Rotman, An Introduction to the Theory of Groups, Springer-Verlag, 1965, 1973, 1984, 1994

Last update: T_KA (03.05.2004)

Syllabus -

1. Representations, equivalences and quasiequivalences.

2. Semidirect products and grups with a normal cyclic subgroup.

3. Splitting, Schur-Zassenhaus Theorem, Hall subgroups.

4. Fratttini subgroup.

5. Groups with a maximal cyclic subgroup.

6. Extraspecial groups.

7. Central products.

8. Generalized Fitting subgroup.

9. Central extensions.

Last update: T_KA (21.05.2004)