[en] With the development of radioactive ion beam facilities and large detector arrays, the study of the structure of heavy nuclei (A > 60) with N ≃ Z have been a subject of intense interest during the last few years. By the limited systematic information for such nuclei, we suggest that these nuclei with A > 60 have different collective behavior from the nuclei with N > Z. The E(4_1"+)/E(2_1"+) values are closed to 2.5. We suggest that these nuclei are gamma unstable ones, These nuclei may be give new insights into neutron - proton(np pair) correlations. Meanwhile, we expect that np pair correlations for nuclei with N ≃ Z are larger than for nuclei N ≥ Z. Many experimental and theoretical works, e.g.[1-13], have been carried out recently for the investigation and understanding of the structure of the nuclei with N ≃ Z. In this paper, we adopt the interacting boson model with isospin (IBM-3) to investigate the band structure and electromagnetic transition properties of the low-lying states in the even-even N = 32 isotones "5"8Fe, "6"0Ni, "6"2Zn and "6"4Ge. The isospin excitation states with T = 0, 1, 2 and 3 are identified, and compared with available data. The E2 and Ml matrix elements for the low-lying states have been investigated. According to this study, the state is the lowest mixed symmetry state in the even-even N = 32 isotones. The agreement between the model calculations and data is reasonably good. (authors)