K. Ding studied a class of Schubert varieties Xλ in type A partial flag manifolds, indexed by integer partitions λ and in bijection with dominant permutations. He observed that the Schubert cell structure of Xλ is indexed by maximal rook placements on the Ferrers board Bλ, and that the integral cohomology groups H∗(Xλ; Z), H ∗(Xμ; Z) are additively isomorphic exactly when the Ferrers boards Bλ,...

All groups considered are finite. Given a group G, the Frattini subgroup of G, Q(G) is defined to be the intersection of all maximal subgroups of G. There has been much interest in generalizing the Frattini subgroup in various ways, and in investigating their influence on the structure of the group (see [3,.5,8,12,13]). These generalizations were done taking into account the following question:...