On Solvability of Noncommutative Power-Associative Nilalgebras

We show that noncommutative power-associative nilalgebras of finite dimension n and nilindex k are solvable if k = n + 1 or k = n. For any given integer n > 2, we present an example of a power-associative nilalgebra of dimension n and nilindex n − 1 which is not solvable. This implies a power-associative nilalgebra of dimension n and nilindex k need not be solvable if k < n.