Groups generated by derangements

We examine the subgroup D ( G ) of a transitive permutation group which is generated by derangements in . Our main results bound index this subgroup: we conjecture that, if has degree n and not Frobenius group, then | : ? ? 1 ; prove except when primitive affine group. For groups, translate our into an equivalent form regarding H R , where linear on finite vector space elements having eigenvalue 1. If kernel, so / isomorphic to complement. give some examples ? group-theoretic structure particular, construct groups