Group Theory

A.Y. 2017/2018
6
Max ECTS
42
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
Aim of this course is to present topics and fundamental theorems concerning Group Theory.
Expected learning outcomes
To read and understand topics In advanced Group Theory.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
To present basic ideas of group theory

1.Reviewing of some standard basic topics on group product ( direct and semidirect product) and on commutator subgroup and its properties. Isomorphism Theorems
2. Group actions Orbits, stabilizers. Sylow's Theorems and applications. Burnside's formula and permutation character. Induced action. Simplicity of some groups
3. Generators and Relations. Generators, Frattini subgroup (Schur's theorem).Finitely generated abelian groups. Free groups. Word problem.
4. Nilpotent and soluble groups. Central series and nilpotent groups, Fitting subgroup. p-nilpotent groups. Fixed point free automorphims and Frobenius Groups. Soluble groups; Carter subgroups. Schmidt-Iwasawa's Theorem.
MAT/02 - ALGEBRA - University credits: 6
Lessons: 42 hours