Nilpotent linear spaces and Albert's Problem

In [8] M.A. Fasoli classified, up to conjugation, all the maximal vector subspaces of M4(C), in which all the elements are nilpotent matrices. This result will allow us to solve Albert's Problem [5] for commutative power-associative C-nilalgebras of dimension n and nilindex n−3 in an affirmative way.