Algebra 2

A.y. 2018/2019
6
Max ECTS
60
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
Aim of this course is the introduction of the principal properties of some algebraic structures: semigroups and groups.
Expected learning outcomes
To produce elementary proofs of properties concerning groups.
Course syllabus and organization

Single session

Responsible
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