Algebra 2

A.Y. 2015/2016
6
Max ECTS
60
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The course is an introduction to Group Theory, in particular to finite groups.
Expected learning outcomes
Knowledge of the basics of Group Theory, with particular emphasis on finite groups.
Course syllabus and organization

Single session

Lesson period
First semester
Course syllabus
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 a cyclic groups.
MAT/02 - ALGEBRA - University credits: 6
Practicals: 33 hours
Lessons: 27 hours
Professors: Bianchi Mariagrazia, Pacifici Emanuele