Bar-Ilan Combinatorics Seminar The next meeting of the seminar will take place, IYH, (when) Sunday, 20 Sivan (June 10), 14:00-15:30 (where) Room 201 (Math & CS Seminar Room), Building 216, Bar-Ilan University (who) Gil Alon (Open University) (what) Semicharacters of groups Abstract: We consider the notion of a semicharacter of a finite group G: It is a function from G to C*, whose restriction to any abelian subgroup is a homomorphism. The set of semicharacters of G is a finite abelian group, that we denote by \hat{G}. This notion extends the notion of the dual group of an abelian group. However, for a nonabelian group G, it is not obvious that \hat{G} is nontrivial. We will prove it; the proof depends on the classification of finite simple groups. We conjecture that the order of \hat{G} is always divisible by the order of G. This conjecture is supported by numerical evidence: We have verified it for all groups of size less than 256. We will show that the conjecture holds for some central families of groups (including the General Linear, Symmetric and Alternating groups), using some "hands on" constructions that rely heavily on the structure of the given group. ************************************************************************* You are all invited! Graduate students are especially welcome. Seminar organizer: Ron Adin <radin@math.biu.ac.il> Seminar's homepage: <http://www.math.biu.ac.il/~radin/comsem/comsem.html> ************************************************************************* --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Adin <radin@math.biu.ac.il>