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We continue developing the theory of nilpotent symplectic alternating algebras. The algebras of upper bound nilpotent class, that we call maximal algebras, have been introduced and well studied. In this paper, we continue with the external case problem of algebras of minimal nilpotent class. We show the existence of a subclass of algebras over a field F that is of certain lower bound class that depends on the dimension only. This suggests a minimal bound for the class of nilpotent algebras of dimension 2 n ≥ 8 of rank 2 over any field. [ABSTRACT FROM AUTHOR]

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 of 2-Engel 3-groups of exponent 27 and under this correspondence we will see that the nilpotent algebras correspond to a subclass of that are those groups in that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of -groups where is an arbitrary prime. [ABSTRACT FROM AUTHOR]

This paper begins the development of a theory of what we will call symplectic alternating algebras. They have arisen in the study of 2-Engel groups but seem also to be of interest in their own right. The main part of the paper deals with the challenging classification of some algebras of this kind which arise in the context of 2-Engel groups and give some new information about these groups. The main result is that there are 31 such algebras with dimension 6 over the field of three elements. [ABSTRACT FROM AUTHOR]

Using known results on 4-Engel groups one can see that a 4-Engel group is locally nilpotent if and only if all its 3-generator subgroups are nilpotent. As a step towards settling the question whether all 4-Engel groups are locally nilpotent we show that all 2-generator 4-Engel groups are nilpotent. [ABSTRACT FROM AUTHOR]