In many-body systems the long range correlations of superfluidity type can be identified by employing the Penrose-Yang criterion, based on density matrix. Using this criterion it will be shown that in N=Z nuclei the pairing interactions as well as general two-body forces induce a transition towards a condensate of alpha-like quartets. Then it will be shown how to represent alpha-like quartets by bosons, through a mapping procedure, and how to treat them in a formalism similar to the interacting boson model (IBM). In this framework we will describe the low-lying bands of 32S, in which we identify a spherical-oblate shape coexistence. The analysis of the potential energy surface indicates that 32S is located at the critical point of the U(5)-SU(3)* phase transition of the IBM structure diagram.