Non Existence of Finite Λ-Submodules of Dual Selmer Groups Over a Cyclotomic ℤp-Extension

The main aim of this note is to give a sufficient condition for the non-existence of non-zero finite submodules for the strict and non-strict Selmer groups over the Iwasawa algebra. These Selmer groups are defined over the cyclotomic ℤ_p-extension of F:=ℚ(μ_p) for p-ordinary representations associated to newforms (see defn (5), (7) and Theorem (3.12)).