We introduce the algebraic structures in particular groups. Groups and their fundamental properties. Subgroups and cosets. Group homomorphisms. Normal subgroups and factor groups. Cyclic groups, linear groups, permutation groups. Lagrange's Theorem, commutators and commutator subgroup. Direct products. Group actions: stabilizers, orbits, transitivity, regularity, Cayley's Theorem. p-groups and Sylow's Theorem. Endomorfisms of cyclic groups and automorfisms of cyclic groups.
Prerequisites for admission
Basics of Algebra studied in Algebra 1
D.Dikranjan, M.S.Lucido Aritmetica e Algebra, Liguori Editore M. Isaacs "Algebra, a graduate course" Brooks /Cole Publishing Company
Assessment methods and Criteria
The final examination consists of two parts: a written exam, an oral exam.
- During the written exam, the student must solve some exercises in the format of open-ended , with the aim of assessing the student's ability to solve problems similar to those done during the course . The duration of the written exam will be proportional to the number of exercises assigned, also taking into account the nature and complexity of the exercises themselves (however, the duration will not exceed three hours). In place of a single written exam given during the first examination session, the student may choose instead to take 2 midterm exams. The outcomes of these tests will be available in the SIFA service through the UNIMIA portal. - The oral exam can be taken only if the written component has been successfully passed. In the oral exam, the student will be required to illustrate results presented during the course in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.
The complete final examination is passed if all two parts (written, oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.