We consider the effect of a coagumented idempotent functorJ in the the category of groups orG-modules where G is a fixed group. We are interested in the ‘extent’ to which such functors change the structure of the objects to which they are applied. Some positive results are obtained and examples are given concerning the cardinality and structure of J(A) in terms of the cardinality and structure ofA, where the latter is a torsion abelian group. For non-abelian groups some partial results and examples are given connecting the nilpotency classes and the varieties of a group G and J(G). Similar but stronger results are obtained in the category of G-modules.
- Localization functors