- I. M. Isaacs, Character theory of finite groups, Academic Press, 1976.
- B. Hupper, Character theory of finite groups, De Gruyter, 1998.
- G. James, M. Liebeck, Representations and characters of groups, Cambridge Mathematics Textbooks, 1993.
Teaching Methods
CFU: 9
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...):
Hours reserved to private study and other indivual formative activities:
Frequency of lectures, practice and lab:
Teaching Tools:
Office hours:
Department of Mathematics "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel:
Email:
alessandro.scarselli@unifi.it, alessandro.scarselli@math.unifi.it
Type of Assessment
Oral exam
Course program
Algebras and modules. Wedderburn's structure theorem. Maschke's theorem.
Group algebras.
Group representations and characters. Orthogonality relations.
Character degrees. Burniside p^aq^b theorem.
Tensor product of modules. Product of characters.
Induced characters. Primitive modules. M-groups. Taketa's theorem.
Permutation modules. Artin's theorem.
Clifford theory. Extension theorems for characters of normal subgroups.
Frobenius groups and Frobenius' theorem.
Ito's theorem. Thompson's theorem.
Structrure of groups with few character degrees.