On solvable $Z_3$-graded alternative algebras

Abstract

Let $A=A_0\oplus A_1\oplus A_2$ be an alternative $Z_3$-graded
algebra.  The main result of the paper is the following: if $A_0$ is
solvable and the characteristic of the ground field not equal 2,3
and 5, then $A$ is solvable.