Subgroup permutability probability conjecture for finite simple classical and alternating groups

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 $\mathfrak{p}(G)$. Subgroup permutability probability conjecture. As $|G|$ tends to infinity, this probability tends to $0$. The conjecture extends a problem of Tărnuceanu and has only been partially addressed by the present paper and related work.