NMAK13019U Representations and Characters of finite Groups (RepChGr)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content

Group representations, group algebras, FG-modules, Maschke's Theorem, Schur's Lemma, irreducible modules, conjugacy classes, characters, inner products of characters, the number of irreducible characters, character tables and orthogonality relations, normal subgroups and lifted characters, tensor products, restriction to a subgroup, induced modules and characters, explicit examples of character tables, permutations and characters, applications to group theory

Learning Outcome

Knowledge: Explain the definitions of concept in the course and operate safely with them. Explain the subject matter described in the table of contents in an insightful way.

Skills: Solve problems in the course subject matter, including the construction of simple character tables. Construct proofs of theorems within the contents of the course.

Competences:  Present and apply abstract results within the content of the course,

LinAlg, Algebra 1
4 hour lectures and 3 hours exercises per week
  • Category
  • Hours
  • Exam
  • 18
  • Guidance
  • 20
  • Lectures
  • 28
  • Preparation
  • 80
  • Theory exercises
  • 60
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
To pass the course you must have the following three activities approved: Two sets of written assignments and one seminar presentation. The seminar presentation will be based on a chapter in the book or a short research paper.
Marking scale
passed/not passed
Censorship form
No external censorship
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.