ALGB Seminar: Daphné Janssens

29/03/2018 - 10:00

Title: Rational and Cut Frobenius Groups

Abstract:
A group G is called cut if the central units of the integral group ring are trivial. This is equivalent to the characterization that the character field Q(χ) of any irreducible complex character χ of G is ’very small’, i.e. is equal to Q or is an imaginary quadratic extension Q(√−d). If only the former case occurs, G is called rational and such groups are the main topic of my talk. More precisely, I will start by presenting some properties and examples of rational groups. Afterwards, I will introduce Frobenius groups and motivate their study from a representation theoretical point of view. Finally I will make the connection between the two subjects, by presenting some results concerning rational and cut Frobenius groups.