Monomial Modules and Endo-Monomial Modules

We determine the multiplicity algebras and multiplicity modules of a p-monomial module. For a general p-group P, we find a sufficient and necessary condition for an endo-monomial P-module to be an endo-permutation P-module, and prove that a capped indecomposable endo-monomial P-module is of p ^′-rank. At last, we give an alternative definition of the generalized Dade P-group.