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
Course program
Artinian rings. Schur Lemma. Radical. Simple Rings. Semisimple rings. Wedderurn Theorem. Algebras. Representations of semisimple algebras. Group algebra. Maschke theorem. Characteers theory. Irreducible characters. Charachters tables. Ortogonality relations. Burnside Theorem. Frobenius reciprocity. Frobenius Kernels and Frobenius complements. Generators and relations. Free group. Presentations of groups. Maximal subgroups. Frattini subgroup. Extensions and cohomology. Frobenius complements. Fusion and transfer. Ditting subgroup. Normal p-complements (Burnside,Frobenius,Thompson). Automorfisms.Semiregular actions. Nilpotency of Frobenius ker.