
Course unit
INTRODUCTION TO GROUP THEORY
SC03111814, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/02 
Algebra 
8.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
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 pronite groups). 
Examination methods:

Oral. The candidate will be asked to present the most important arguments presented in the course, proving the more signicant results and solving some related exercise. 
Assessment criteria:

Check of the learning of the taught notions and on the ability of their application. 
Course unit contents:

General introduction to group theory: actions of groups, solvable and nilpotent groups, finitely presented groups. A short history of the classication of finite simple groups. Topological groups, profinite groups (characterizations, profinite completion, countable based pronite groups, arithmetical properties, subgroups of finite index in pronite groups, Galois groups of infinite 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). 
Textbooks (and optional supplementary readings) 

I.M. Isaacs, Finite group theory. Providence, Rhode Island: American Mathematical Society, 2008.

J. Wilson, Profinite groups. Oxford: Clarendon Press, 1998.

Innovative teaching methods: Teaching and learning strategies
Sustainable Development Goals (SDGs)

