# fully invariant subgroup

A subgroup $H$ of a group $G$ is fully invariant if $f(H)\subseteq H$ for all endomorphisms $f\colon G\to G$. Such a subgroup is also called fully characteristic.

This is a stronger condition than being a characteristic subgroup.

The derived subgroup is fully invariant.

 Title fully invariant subgroup Canonical name FullyInvariantSubgroup Date of creation 2013-03-22 13:13:07 Last modified on 2013-03-22 13:13:07 Owner mclase (549) Last modified by mclase (549) Numerical id 6 Author mclase (549) Entry type Definition Classification msc 20D99 Related topic CharacteristicSubgroup Related topic SubnormalSubgroup Related topic ExampleOfFullyInvariantSubgroup Defines fully invariant Defines fully characteristic Defines fully characteristic subgroup