A family of transitive modular Lie superalgebras with depth one

The embedding theorem is established for Z-graded transitive modular Lie superalgebras g = circle plus-1 <= i <= rg(i) satisfying the conditions: (i) g(0) similar or equal to p(g-1) and g(0)-module g(-1) is isornorphic to the natural p(g(-1))-module; (ii) dim g(1) = 2/3n(2n(2) + 1), where n = 1/2 dim g(-1). In particular, it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isornorphic to the odd Hamiltonian superalgebras. The restricted Lie superalgebras are also considered.