Course MAT-40-34-K-4
Character Theory of Finite Groups; p-adic Numbers (4V+2U, 9.0 LP)
Course Type
SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
---|---|---|---|---|---|
- | K | Lecture with exercise classes (V/U) | |||
4 | V | Lecture | 6.0 CP | 56 h | 124 h |
2 | U | Exercise class (in small groups) | 3.0 CP | 28 h | 62 h |
(4V+2U) | 9.0 CP | 84 h | 186 h |
Basedata
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
The certificate for the exercises ("Übungsschein") consists of the two (partial) certificates for the exercises in the courses [MAT-40-25-K-4] and [MAT-40-24-K-4].
Contents
Character Theory of Finite Groups:
- Maschke's theorem,
- character tables,
- orthogonality relations,
- rationality questions,
- Burnside theorem,
- induced characters,
- Frobenius groups.
p-adic Numbers:
- construction of p-adic numbers,
- p-adic integers, units,
- p-adic topology,
- Hensel's lemma,
- algebraic closure,
- Newton polygon,
- inertia and ramification groups
Competencies / intended learning achievements
In the part "Character Theory of Finite Groups", the students have studied the basic terms, propositions and techniques of representation theory through the character theory of finite groups. In particular, they have learnt to work with generic characters and character tables.
In the part "p-adic Numbers", the students have studied extensions of a number system through p-adic numbers which are fundamental for number theory. In particular, they have studied their main properties and some simple applications.
Literature
Character Theory of Finite Groups:
- M. Isaacs: Character Theory of Finite Groups,
- G. James, M. Liebeck: Representations and Characters of Finite Groups,
- J. Alperin, R. Bell: Groups and Representations.
p-adic Numbers:
- I.N. Stewart, D.O. Tall: Algebraic Number Theory,
- M. Trifković: Algebraic Theory of Quadratic Numbers.
Materials
Further literature will be announced in the lecture; Exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)
Requirements for attendance (informal)
Knowledge from the course [MAT-12-21-K-3] is useful but not necessarily required.
Modules:
Courses
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
Requirements for attendance (formal)
None
References to Course [MAT-40-34-K-4]
Course-Pool | Name | ||
---|---|---|---|
[MAT-40-4V-KPOOL-4] | Elective Courses Algebra, Geometry and Computeralgebra (4V, B.Sc.) | ||
[MAT-40-KPOOL-4] | Specialisation Algebra, Geometry and Computer Algebra (B.Sc.) |
Notice