Abstract: A Symplectic Alternating Algebra is a symplectic vector space , whose associated alternating form is nondegenerate, that is furthermore equipped with a binary alternating product with the extra requirement that .

These linear structures originate from a study of powerful 2-Engel groups and there is a 1-1 correspondence between a rich class of powerful 2-Engel 3-groups of exponent 27 and Symplectic Alternating Algebras over the field of 3 elements.

We will give an overview of these and then focus on a recent result that states that any finite group can be realised as the automorphism group of some Symplectic Alternating Algebra.