Algebra Seminar talk
2010-10-15
Peter P. Palfy
The number of conjugacy classes in some matrix groups
Abstract:
A famous open problem due to Graham Higman asks if the number of
conjugacy classes in the group of nxn unipotent upper triangular
matrices over the q-element field can be expressed as a polynomial
function of q for every fixed n. We consider the generalization of
the problem for the so-called pattern groups (where some entries of
the matrix are set to be 0) and prove that for some patterns the
number of conjugacy classes in the corresponding pattern groups is
not a polynomial function of q. It is a joint work with Zoltán Halasi.