Abstract Two groups L 1 L₁ and L 2 L₂ are compatible if there exists a finite group 𝐺 with isomorphic normal subgroups N 1 N₁ and N 2 N₂ such that L 1 ≅ G / N 1 L₁ G/N₁ and L 2 ≅ G / N 2 L₂ G/N₂. In this paper, we give new necessary conditions for two groups to be compatible.
Ding et al. (Fri,) studied this question.