MD131 Representations of groups

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Jiří Kaďourek, CSc.
Prerequisites
(( M1110 Linear Algebra I || M1115 Linear Algebra I ) && ( M2150 Algebra I || M2155 Algebra 1 )) || PROGRAM(N-MA) || PROGRAM(D-MA)
This subject is accessible to students having a solid knowledge of the fundamentals of the theory of groups, being acquainted with the basic notions from the theory of rings and fields, being well familiar with the foundations of linear algebra and willing to solidify and integrate their knowledge of these areas of algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course focuses on the theory of representations of finite groups by regular linear transformations of finite dimensional vector spaces. In other words, one is concerned with the study of homomorphisms of finite groups into general linear groups. The general linear group is defined to be the group of all regular linear transformations of a given finite dimensional vector space. Attention is concentrated to the case when the vector space in question is a vector space over an algebraically closed field of characteristic zero. This case encompasses the classical theory of characters of finite groups. These topics form an indispensable part of every course aimed at a deeper understanding of the theory of groups. Additionally, these ideas have profound implications in the theory of finite groups. Just name the Burnside p-q theorem, and the theorem of Frobenius that until now cannot be established without invoking the character theory of finite groups.
Literature
  • ALPERIN, J. L. and Rowen B. BELL. Groups and representations. New York: Springer-Verlag, 1995, x, 194 s. ISBN 0-387-94525-3. info
  • ROBINSON, Derek John Scott. A course in the theory of groups. 2nd ed. New York: Springer-Verlag, 1995, xvii, 499. ISBN 0387944613. info
  • GORENSTEIN, Daniel. Finite Groups. Second edition. New York: Chelsea Publishing Co., 1980, xvii, 519. ISBN 0-8284-0301-5. info
  • DUMMIT, David Steven and Richard M. FOOTE. Abstract algebra. 2nd ed. Upper Saddle River, N.J.: Prentice Hall, 1999, xiv, 898 s. ISBN 0-13-569302-0. info
Assessment methods (in Czech)
Předmět je ukončen ústní zkouškou. Důraz je kladen na orientaci v základních principech teorie reprezentací konečných grup.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught only once.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007, Autumn 2012, Spring 2019.