  Stefan M$\ddot{\mathrm{u}}$ller posed the problem "Do Hofer's metrics on the
group of Hamiltonian diffeomorphism and the one of Hamiltonian homeomorphisms
(Hameomorphisms) correspond?". Let $(M,\omega)$ be a compact exact symplectic
manifold. We prove that the group of Hamiltonian homeomorphisms is not a simple
group if the positive answer of M$\ddot{\mathrm{u}}$ller's question holds . To
prove this results, we introduce fragmented Hofer's norms on a normal subgroup
of the group of Hamiltonian homeomorphisms.
