Let be a finitedimensional Lie algebra over the
field . The AdoIwasawa Theorem asserts the existence
of a finitedimensional module which gives a faithful representation of . Let be a subnormal subalgebra of , let be a saturated formation of soluble Lie algebras
and suppose that . I show that there exists a module with the extra property that it is hypercentral as module. Further, there exists a module
which has this extra property simultaneously for
every such
and , along with the Hochschild extra that
is nilpotent for every with nilpotent. In particular,
if is supersoluble, then it has a faithful
representation by upper triangular matrices.
