  We introduce quantum procedures for making $\cal G$-invariant the dynamics of
an arbitrary quantum system S, where $\cal G$ is a finite group acting on the
space state of S. Several applications of this idea are discussed. In
particular when S is a N-qubit quantum computer interacting with its
environment and $\cal G$ the symmetric group of qubit permutations, the
resulting effective dynamics admits noiseless subspaces. Moreover it is shown
that the recently introduced iterated-pulses schemes for reducing decoherence
in quantum computers fit in this general framework. The noise-inducing
component of the Hamiltonian is filtered out by the symmetrization procedure
just due to its transformation properties.
