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.
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