| Area of Mathematics: | Algebra & Geometry (EAG) | ||
| Semester: | 5th | ||
| Course ID: | 52202 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS: | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Istructors: | Kapetanakis Giorgos | ||
Description
- Definitions and basic properties of groups, order, subgroups, Lagrange theorem, normal subgroups, quotient group.
- Group presentation with generators and relations, free groups.
- Cyclic groups. Dihedral groups, permutation groups. Decomposition of a permutation into cycles. Conjugate subgroups, conjugacy classes of group elements, conjugacies of the symmetric group.
- Isomorphism theorems, Cayley’s theorem.
- Quotient groups, product of groups, group extensions.
- Classification of finitely generated abelian groups.
- Group actions, orbit counting, Cauchy’s theorem
- Sylow’s theorems.
- Normal, solvable and nilpotent groups.
Bibliography
- M. Armstrong. Groups and Symmetry. Springer, 1988.
