Charlotte Scott Centre for Algebra

**will give a talk**

*Symplectic Alternating Algebras and their groups of automorphisms*at the Algebra seminar on 20 January 2016, Wednesday, at 4pm (room ENG209 in Engineering hub, building 13 on the uni map).*Abstract:* A Symplectic Alternating Algebra is a symplectic vector space $latex L$, whose associated alternating form is nondegenerate, that is furthermore equipped with a binary alternating product with the extra requirement that $latex (xy,z)=(yz,x)$.

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.

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