Summary: Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial.
In this paper we show that this is a special case of a product rule. The product rule enables us to calculate the Thom polynomials of singularities if we know the Thom polynomial of the product singularity. As a special case of the product rule we define a formal power series (Thom series, \(\text{Ts}_{Q})\) associated with a commutative, complex, finite dimensional local algebra \(Q\), such that the Thom polynomial of every singularity with local algebra \(Q\) can be recovered from \(\text{Ts}_{Q}\).