The derivation problem for one type of bimodules over group algebras

The derivation problem is a familiar one concerning group algebras, particularly $L_1(G)$ and von Neumann algebras. In this paper, we study the Banach bimodule ${\mathrm{\ell }}_p(G)$, which is generated by the ${\mathrm{\ell }}_p$ norm over a specific class of groups with well-organized conjugacy classes. For this case, we will demonstrate that all ${\mathrm{\ell }}_p(G)$ derivations are inner.