Orthogonal groups and periodicity of links

We study cyclic subgroups of orthogonal groups over Z_p and Z_{p^k}. We show what is the maximal r such that Z_{q^r} is a subgroup of the given orthogonal group. We apply this to obtain a periodicity criterion for links. This is a joint project with Przemysław Grabowski, Adam Król and Maria Marchwicka.