Algebra 2

A.Y. 2018/2019
Lesson for
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.
To produce elementary proofs of properties concerning groups.

Course structure and Syllabus

Active edition
Yes
Responsible
MAT/02 - ALGEBRA - University credits: 6
Practicals: 33 hours
Lessons: 27 hours
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.
Lesson period
First semester
Lesson period
First semester