Intersecting families in the alternating group and direct product of symmetric groups (Q871132)

Summary: Let \(S_n\) denote the symmetric group on \([n]=\{1, \dots, n\}\). A family \(I \subseteq S_n\) is intersecting if any two elements of \(I\) have at least one common entry. It is known that the only intersecting families of maximal size in \(S_n\) are the cosets of point stabilizers. We show that, under mild restrictions, analogous results hold for the alternating group and the direct product of symmetric groups.