A classification of the maximal subgroups of the finite alternating and symmetric groups

Bounds for the probability of generating the symmetric and alternating groups

“…By [15], a maximal subgroup G of X which is different from an almost simple primitive group is either wreath product primitive, affine primitive, or diagonal primitive, and has the form G = H ∩ X where H is a maximal subgroup of S n of the same type as G.…”

The imprimitive faithful complex characters of the Schur covers of the symmetric and alternating groups

“…[17]). Again as every imprimitive and transitive subgroup of A n is contained in an imprimitive and transitive maximal subgroup of S n , the imprimitive and transitive maximal subgroups of A n have the form ðS n=k o S k Þ V A n , where k is as above.…”

Homogeneous factorisations of Johnson graphs

“…By Proposition 2.10, A q+1 is arc-transitive and so A q+1 M . Thus by [18], M PΓL(2, q) (recall that q is even). Thus G = PΓL(2, q) = G and hence g ∈ G. Hence E 1 = E 2 and so the homogeneous factorisations obtained from Construction 3.10 are pairwise non-isomorphic.…”