Normal subgroups whose conjugacy class graph has diameter three

Let G be a finite group and let N be a normal subgroup of G. We determine the structure of N when the diameter of the graph associated to the G-conjugacy classes contained in N is as large as possible, that is, equal to three.The research of the first and the second authors is supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and the third authors are also partially supported by Universitat Jaume I, grant P11B2015-77.Beltran, A.; Felipe Román, MJ.; Melchor, C. (2016). Normal subgroups whose conjugacy class graph has diameter three. Bulletin of the Australian Mathematical Society. 94(2):266-272. doi:10.1017/S0004972715001860S26627294