  We study finite-dimensional nonassociative algebras. We prove the implicit
function theorem for such algebras. This allows us to establish a
correspondence between such algebras and quasigroups, in the spirit of
classical correspondence between divisible torsion-free nilpotent groups and
rational nilpotent Lie algebras. We study the related questions of the
commensurators of nilpotent groups, filiform Lie algebras of maximal
solvability length and partially ordered algebras.
