12.50 (1992)

(Well-known problem). Find an algorithm which decides, by a given finite set of matrices in $SL_3(\mathbb{Z})$, whether the first matrix of this set is contained in the subgroup generated by the remaining matrices. An analogous problem for $SL_4(\mathbb{Z})$ is insoluble since a direct product of two free groups of rank 2 embeds into $SL_4(\mathbb{Z})$.