  In this talk we describe very briefly how Gritsenko and Nikulin classified in
\cite{3} the generalised Cartan matrices of rank 3, of elliptic type (so they
have the generalised lattice Weyl vector), which are twisted to symmetric
generalised Cartan matrices. We then introduce a conjecture on this
classification and propose an algorithm for attacking it. The author would like
to thank prof. V.V. Nikulin for giving him the opportunity to study this
subject.

Group Theory