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.