### On local weak crossed product orders

Let Λ = (S/R,α) be a local weak crossed product order in the crossed product algebra A = (L/K,α) with integral cocycle, and $H=\sigma \in Gal(L/K)|\alpha (\sigma ,{\sigma}^{-1})\in S*$ the inertial group of α, for S* the group of units of S. We give a condition for the first ramification group of L/K to be a subgroup of H. Moreover we describe the Jacobson radical of Λ without restriction on the ramification of L/K.