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Course, academic year 2017/2018
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Combinatorial Group Theory 1 - NMAG431
Czech title: Kombinatorická teorie grup 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 1
Hours per week, examination: winter s.:2/0 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Pavel Růžička, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG033
Interchangeability : NALG033
Is co-requisite for: NMAG432
Annotation -
Last update: T_KA (09.05.2013)

Winter term: Subgroups of free groups (Nielsen's and Reidemaister's method), Tietze transformations, HNN extensions, free products with an amalgamated subgroup, geometrical methods, Cayley complexes. Spring term: Other selected topics in elementary combinatorical group theory.
Literature -
Last update: Mgr. et Mgr. Jan Žemlička, Ph.D. (06.09.2013)

R. Lyndon a P. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977.

W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory, Wiley, 1966.

J. J. Rotman, An Introduction to The Theory of Groups, Springer-Verlag, Druhé vydání 1999.

Syllabus -
Last update: Mgr. et Mgr. Jan Žemlička, Ph.D. (06.09.2013)

1. Free group, subgroups of a free group (the method of Nielsen and Reidemeister), the relationship between the index and the rank of subgroup of a group

of a finite index, subgroups of finite rank as free factors in a subgroup of a finite index. Conjugation and cyclically reduced words.

2. Tietze transformations.

3. HNN extensions, defining relations, Britton's lemma and the normal form theorem, applications of HNN extensions.

4. Free products with an amalgamated subgroup, defining relations, the normal form theorem.

5. Geometrical methods, the fundamental group of a two-dimensional complex, application for a geometrical proof that a subgroup of a free group is free,

Kurosh's theorem, Grushko -- von Neumann's theorem.

6. Cayley complexes

 
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