- 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.
Learning Objectives
The course aims to provide the students with fundamental knowledge and understanding in Character Theory of Finite Groups.
Teaching Methods
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Training sessions: training of the students to modelling and solving a wide selection of problems in Character Theory . The training sessions are conducted so to:
-- help the students develop communication skills and apply the theoretical knowledge;
-- encourage independent judgement in the students.
Moodle learning platform: online teacher-student interaction, posting of additional notes, weekly exercise sheets, copies of past tests.
Remark: The suggested reading includes supplementary material that may be useful for further personal studies in mathematics or in any scientific subject.
Further information
Department of Mathematics "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
For further information please contact:
Tel: +39 055 2751443
Email:
dolfi@math.unifi.it
Type of Assessment
Oral examination: A number of questions are posed. The oral examination is designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication skills, critical thinking and appropriate use of mathematical language.
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.