The notion of minimal complements was introduced by Nathanson in 2011. Since then, the existence or the inexistence of minimal complements of sets have been extensively studied. Recently, the study of inverse problems, i.e., which sets can or cannot occur as minimal complements has gained traction. For example, the works of Kwon, Alon–Kravitz–Larson, Burcroff–Luntzlara and also that of the authors, shed light on some of the questions in this direction. These works have focussed mainly on the group of integers, or on abelian groups. In this work, our motivation is two-fold:

(1)

to show some new results on the inverse problem,

(2)

to concentrate on the inverse problem in not necessarily abelian groups.

最小补的概念是由 Nathanson 在 2011 年提出的。从那时起，集合的最小补的存在或不存在得到了广泛的研究。最近，对逆问题（即哪些集合可以或不可以作为最小补集出现）的研究受到了关注。例如，Kwon、Alon-Kravitz-Larson、Burcroff-Luntzlara 的作品以及作者的作品，阐明了这个方向的一些问题。这些工作主要集中在整数群或阿贝尔群上。在这项工作中，我们的动机有两个：

(1)

显示一些关于逆问题的新结果，

(2)

专注于不一定是阿贝尔群的逆问题。