  We solve the dynamics of an open quantum system where N strongly driven
two-level atoms are equally coupled on resonance to a dissipative cavity mode.
Analytical results are derived on decoherence, entanglement, purity, atomic
correlations and cavity field mean photon number. We predict decoherence-free
subspaces for the whole system and the N-qubit subsystem, the monitoring of
quantum coherence and purity decay by atomic populations measurements, the
conditional generation of atomic multi-partite entangled states and of cavity
cat-like states. We show that the dynamics of atoms prepared in states
invariant under permutation of any two components remains restricted within the
subspace spanned by the completely symmetric Dicke states. We discuss examples
and applications in the cases N=3,4.
