Algebra 2
A.Y. 2018/2019
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.
Lesson period: First semester
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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.
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
Lessons: 27 hours
Professors:
Bianchi Mariagrazia, Pacifici Emanuele