Is the product of two locally soluble groups is locally soluble? > A group $G$ is locally soluble if all finitely generated subgroups are soluble. My question is the class of locally soluble group is it $N

Is the product of two locally soluble groups is locally soluble? > A group $G$ is locally soluble if all finitely generated subgroups are soluble. My question is the class of locally soluble group is it $N_0$-closed?If it is no is there contre example?and what class of group the property is true.

The class of locally soluble group is not $N_0$-closed. P.Hall has given an (unpublished) example described in Part 2 of Robinson's "Finiteness Conditions and Generalized Soluble Groups". Theorem 8.19.1 on page 91.