Second Level Degree in Mathematics
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INTRODUCTION TO GROUP THEORY - 8 CFU
Teacher
Andrea Lucchini
Scheduled Period
I Year - 1 Semester | 04/10/2021 - 15/01/2022
Hours: 64 (32 esercitazione, 32 lezione)
Prerequisites
Basic knowedges in general algebra
Target skills and knowledge
We will give a general introduction to the theory of group, describing methods and results. In the second part of the course we will concentrate on particular topics (for example pro*nite groups).
Examination methods
Oral. The candidate will be asked to present the most important arguments presented in the course, proving the more signi*cant results and solving some related exercise.
Assessment criteria
Check of the learning of the taught notions and on the ability of their application.
Course contents
General introduction to group theory: actions of groups, solvable and nilpotent groups, fi*nitely presented groups. A short history of the classi*cation of *finite simple groups. Topological groups, pro*finite groups (characterizations, pro*finite completion, countable based pro*nite groups, arithmetical properties, subgroups of *finite index in pro*nite groups, Galois groups of in*finite dimensional extension). Probabilistic methods in group theory.
Planned learning activities and teaching methods
Standar lectures at the blackboard, with exercises (solved in part by the students themseves).