M7170 Algebraic Seminar

Faculty of Science
Autumn 2009
Extent and Intensity
0/2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 MS1,01016
Prerequisites
M2150 Algebra I || M2155 Algebra 1 || ( FI:MB008 Algebra I ) || PROGRAM ( N - MA ) || PROGRAM ( 1433:N - IN )
Algebra: groups, rings, vector spaces
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 16 student(s).
Current registration and enrolment status: enrolled: 0/16, only registered: 0/16, only registered with preference (fields directly associated with the programme): 0/16
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Discrete Mathematics)
  • Mathematics (programme PřF, N-MA, specialization Discrete Mathematics)
Course objectives
The seminar offers an active acquaitance with some important aspects of modern algebra. As a rule, selected more advanced topics in group theory are included in the programme of the seminar. After passing this seminar the student should be able to read up all by himself more exacting subjects from literature, particularly from various areas of contemporary algebra, and he should be able to report on them in an understandable way before the audience.
Syllabus
  • Selected topics in group theory.
  • Among others, the following subjects are covered:
  • Semidirect products of groups.
  • The Kaloujnine-Krasner theorem.
  • Group actions on sets.
  • Sylow subgroups and Sylow's theorem.
  • The Jordan-Hölder theorem.
  • Nilpotent and solvable groups.
  • P. Hall's theorem on finite solvable groups.
  • The Schur-Zassenhaus theorem.
Literature
  • An introduction to the theory of groups. Edited by Joseph J. Rotman. 4th ed. New York: Springer-Verlag, 1995, xvi, 513. ISBN 0387942858. info
  • ROBINSON, Derek John Scott. A course in the theory of groups. 2nd ed. New York: Springer-Verlag, 1995, xvii, 499. ISBN 0387944613. info
  • ALPERIN, J. L. and Rowen B. BELL. Groups and representations. New York: Springer-Verlag, 1995, x, 194 s. ISBN 0-387-94525-3. info
  • COHN, P. M. Algebra. Vol. 3. 2nd ed. Chichester: John Wiley & Sons, 1996, xii, 474 s. ISBN 0-471-96106-43. info
Teaching methods
The seminar takes its course in the form of reports presented by the students.
Assessment methods
In order to fulfill the requirements, the student is asked to participate actively in the course of events at the seminar and to present therein some of the seminar's topics in the form of an individual report.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Spring 2019, Spring 2021, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2009, recent)
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