Abstract
Some algebraic structures are isomorphic to their substructures but it is not always true. Some times they are isomorphic to their substructures with certain properties. Grinshpon et. al. investigated abelian groups which are isomorphic to their subgroups with certain properties.This interesting fact motivates us to investigate QTAG-modules which are isomorphic to their proper submodules with special conditions. Here we study If-modules which are isomorphic to their fully invariant submodules. We define admissible sequence of the Ulm-Kaplansky invariants to define If-module and investigate their properties.