Character Theory of Finite Groups; p-adic Numbers (4V+2U, 9.0 LP)
|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|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Maschke's theorem,
- character tables,
- orthogonality relations,
- rationality questions,
- Burnside theorem,
- induced characters,
- Frobenius groups.
- 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 "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.
- M. Isaacs: Character Theory of Finite Groups,
- G. James, M. Liebeck: Representations and Characters of Finite Groups,
- J. Alperin, R. Bell: Groups and Representations.
- I.N. Stewart, D.O. Tall: Algebraic Number Theory,
- M. Trifković: Algebraic Theory of Quadratic Numbers.
Requirements for attendance (informal)
- [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)