In a groundbreaking paper, Ellis, Friedgut and Pilpel showed that $t$-intersecting families of permutations contain at most $(n-t)!$ permutations, for large enough $n$. They also identified the extremal families: they are all $t$-cosets.
Unfortunately, Section 5 of the paper, which identifies the extremal families, is wrong. Fortunately, the identification follows from a different paper of Ellis, which is already mentioned in the original paper. A different proof follows from our work on complexity measures on the symmetric group.