# Non-existence of a short algorithm for multiplication of 3×3 matrices with group S_4× S_3, II

It is proved that there is no an algorithm for multiplication of 3×3 matrices of multiplicative length ≤23 that is invariant under a certain group isomorphic to S_4× S_3. The proof makes use of description of the orbits of this group on decomposable tensors in the tensor cube (M_3(ℂ))^⊗3 which was obtained earlier.

READ FULL TEXT