Groups and subgroups. Normal subgroups. Factor groups. Isomorphism theorems. Actions and permutation groups. Sylow theorems. Field extensions. Algebraic and trascendental extensions. Degree of an extension. Splitting fields, normal extensions and Galois extensions. Galois group. Galois correspondence. Finite fields.
Knowledge acquired:
Basics of group theory, concept of group action, elements of Galois’
theory, application of acquired knowledge for solving problems.
Skills acquired (at the end of the course):
The student will be able to solve basic problems in the theory of groups,
fields and equations
Prerequisites
Courses required: Algebra I
Courses recommended: Geometry I
Teaching Methods
CFU: 6
Total hours of the course (including the time spent in attending lectures,
seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities:
84
Further information
Frequency of lectures, practice and lab: Recommended
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Type of Assessment
Written and oral exams
Course program
Groups and subgroups. Normal subgroups. Factor groups. Isomorphism theorems. Actions and permutation groups. Sylow theorems. Field extensions. Algebraic and trascendental extensions. Degree of an extension. Splitting fields, normal extensions and Galois extensions. Galois group. Galois correspondence. Finite fields.