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fully invariant subgroup (Definition)

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.



"fully invariant subgroup" is owned by mclase.
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See Also: characteristic subgroup, subnormal subgroup, example of fully invariant subgroup

Also defines:  fully invariant, fully characteristic, fully characteristic subgroup

Attachments:
example of fully invariant subgroup (Example) by juanman
example of a non-fully invariant subgroup (Example) by Algeboy
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Cross-references: derived subgroup, characteristic subgroup, endomorphisms, group, subgroup
There are 9 references to this entry.

This is version 3 of fully invariant subgroup, born on 2002-12-07, modified 2004-03-22.
Object id is 3684, canonical name is FullyInvariantSubgroup.
Accessed 4940 times total.

Classification:
AMS MSC: 20D99 (Group theory and generalizations :: Abstract finite groups :: Miscellaneous)
Pending Errata and Addenda
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