Group Theory
| Title | ΘΕΩΡΙΑ ΟΜΑΔΩΝ / Group Theory |
| Code | 0131 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Coordinator | Athanasios Papistas |
| Common | Yes |
| Status | Active |
| Course ID | 40000300 |
Programme of Study: Merikīs Foítīsīs
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 1
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
| Academic Year | 2016 – 2017 |
| Class Period | Winter |
| Faculty Instructors | |
| Class ID | 600038168
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600038168
- At the Website of the School:
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
The students are in position to apply the basic notions of Group Theory to practise.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Work autonomously
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Group action on sets and groups (permutation representation, Orbits, Stabilizers, Lemma Orbit-Stabilizer), Burnside’s Lemma, Transitive action, Group action by conjugation (normalizer, centralizer), semi-direct product of groups (Dihedral groups), Abelian groups (Free abelian group of finite rank, torsion-free abelian group, torsion abelian group), The decomposition theorem of finitely generated abelian groups (decomposables and indecomposables), Sylow’s Theorems (counting and cyclic methods), Simple groups, Groups of small order, Soluble groups (Derived group, Derived series, normal series, Soluble series), Solvability of Sn.
Keywords
Action, Sylow Theorems, Abelian groups, Series, Soluble groups
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 26 | ✓ | |||
| Tutorial | 13 | ✓ | |||
| Total | 39 |
Student Assessment
Description
Examinations
Student Assessment methods
- Written Assignment (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Εισαγωγή στην Άλγεβρα, J. Fraleigh
Σημειώσεις στη Θεωρία Ομάδων, Α.Ι. Πάπιστας
Last Update
19-09-2013
