2 problems

Let $G$ be a finite group, and let $\mathfrak{p}(G)$ denote its subgroup permutability degree. Subgroup permutability degree criterion. If … then $G$ is not simple. This is present…

Let $G$ be a finite simple classical or alternating group. The probability that two subgroups of $G$ permute is the subgroup permutability degree of $G$, denoted $\mathfrak{p}(G)$.…