fully invariant subgroup

A subgroup $H$ of a group $G$ is fully invariant if $f(H)\subseteq H$ for all endomorphisms $f:G\to G$. 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