On Commutative Power-Associative Nilalgebras

We prove that every commutative power-associative nilalgebra of dimension n and nilindex ≥n − 2 is solvable. In this case, the algebra is over a field F of characteristic zero or of sufficiently high characteristic compared to the nilindex. We show that every commutative nilalgebra (not necessarily power-associative algebra) of dimension ≤6 over a field of characteristic ≠2, 3, 5 is solvable.