Within series II we extend the theory of maximal nilpotent substructures
to solvable associative algebras, especially for their group of units
and their associated Lie algebra. We construct all maximal nilpotent Lie
subalgebras and characterize them by simple and double centralizer
properties. They possess distinctive attractor and repeller
characteristics. Their number of isomorphic classes is finite and can be
bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are
extremal among all maximal nilpotent Lie subalgebras. The maximal
nilpotent Lie subalgebras are connected to the maximal nilpotent
subgroups. This correspondence is bijective via forming the group of
units and creating the linear span. Cartan subalgebras and Carter
subgroups as well as the Lie nilradical and the Fitting subgroup are
linked by this correspondence. All partners possess the same class of
nilpotency based on a theorem of Xiankun Du. By using this
correspondence we transfer all results to maximal nilpotent subgroups of
the group of units. Carter subgroups and the Fitting subgroup turn out
to be extremal among all maximal nilpotent subgroups. All four extremal
substructures are proven to be Fischer subgroups, Fischer subalgebras,
nilpotent injectors and projectors. Numerous examples (like group
algebras and Solomon (Tits-) algebras) illustrate the results to the
reader. Within the numerous exercises these results can be applied by
the reader to get a deeper insight in this theory.
