Arnold's seminar 28.09.99 M. Kazarian "Computing Thom polynomials via symmetries of singularities (after a paper by R. Rimanyi)" Every fixed type of singularities of a smooth map of manifolds form a cycle whose Poincare dual cohomology class is called the Thom polynomial. The classical problem of computing this polynomial is not solved in many cases. One quite simple observation concerning symmetries of singularities gives a new very powerful method of its computation. This method as well as many examples are explained.