Advances in Just-Non-$\mathfrak{X}$ Groups and Minimal Non-$\mathfrak{X}$ Groups

Abstract

Let $\mathfrak{X}$ be a class of groups. A group which does not belong to $\mathfrak{X}$ but all of whose proper quotients belong to $\mathfrak{X}$ is called Just-Non-$\mathfrak{X}$ group. A group which does not belong to $\mathfrak{X}$ but all of whose proper subgroups belong to $\mathfrak{X}$ is called Minimal-Non-$\mathfrak{X}$ group. Just-Non-$\mathfrak{X}$ groups and Minimal-Non-$\mathfrak{X}$ groups are correlated by structural results for different choices of the class $\mathfrak{X}$. Many authors investigated these groups and there is a long standing line of research