10.10.2011 Lecturer: dr. Sergei Evdokimov (Petersburg Department of V.A.Steklov Institute of Mathematics, St. Petersburg, Russia)

Title:  Characterization of Cyclic Schur Groups

Abstract:  We say that a finite group G is a Schur group if every S-ring over it is schurian, i.e. determined by a suitable permutation group on G containing the regular subgroup of right translations. Here under an S-ring over G we mean a subalgebra of the group algebra QG that contains 1_G and is closed with respect to the componentwise multiplication and inversion. In the talk a complete characterization of cyclic Schur groups is given. It follows that the smallest non-Schur cyclic group has order 72. The proof is based on the theory of circulant S-rings and on the criteria of schurity and non-schurity for them. (joint work with I. Kov´acs and I. Ponomarenko).

Slides from the talk are avalilable here: DOWNLOAD!