Algebra Seminar talk
Peter P. Palfy
The number of conjugacy classes in some matrix groups
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.