  A subalgebra pair of semisimple complex algebras B < A with inclusion matrix
M is depth two if MM^t M < nM for some positive integer n and all corresponding
entries. If A and B are the group algebras of finite group-subgroup pair H < G,
the induction-restriction table equals M and S = MM^t satisfies S^2 < nS iff
the subgroup H is depth three in G; similarly depth n > 3 by successive right
multiplications of this inequality with alternately M and M^t. We show that a
Frobenius complement in a Frobenius group is a nontrivial class of examples of
depth three subgroups. Depth-3 towers of Hopf algebras are also considered: a
tower of Hopf algebras A > B > C is shown to be depth-3 if C < core(B).
