Nilpotent symplectic alternating algebras II

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras correspond to a subclass of C that are those groups in C that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of p-groups where p is an arbitrary prime.