INTRODUCTION TO GROUP THEORY

Second cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: First Semester

Lecturer: ANDREA LUCCHINI

Number of ECTS credits allocated: 8


Syllabus
Prerequisites: Basic knowedges in general algebra
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.
Course unit 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.