  The heaviest N=Z doubly-magic nucleus, $^{100}$Sn, and the neighboring nuclei
offer unique opportunities to investigate the properties of nuclear interaction
in extreme conditions. In particular, the Cd isotopes are expected to present
features similar to those found in the Sn isotopic chain, since they have only
two proton holes in the Z=50 shell.
  In this manuscript, the lifetime measurements of low-lying states in the
even-mass $^{102-108}$Cd is presented. Thanks to the powerful detection
capabilities of AGATA array and VAMOS++ spectrometer, the unusual employment of
multi-nucleon transfer reactions permitted to investigate the first 2$^+$ and
4$^+$ states in all these nuclei, together with various deformed bands in
$^{106}$Cd. The results were interpreted in the context of new state-of-the-art
beyond-mean-field calculations, using the symmetry-conserving
configuration-mixing approach.
  Despite the similarities in the electromagnetic properties of the low-lying
states, there is a fundamental structural difference between the ground-state
bands in the Z=48 and Z=50 isotopes. The comparison between experimental and
theoretical results revealed a rotational character of the Cd nuclei, which
have prolate-deformed ground states with $\beta_2 \approx 0.2$. At this
deformation Z=48 becomes a closed-shell configuration, which is favored with
respect to the spherical one.
