Source: wikibot/characteristic-subgroup
= Characteristic subgroup
{wiki=Characteristic_subgroup}
A **characteristic subgroup** of a group \\( G \\) is a subgroup \\( H \\) that is invariant under all automorphisms of the group \\( G \\). This means that for any automorphism \\( \\phi \\) of \\( G \\), the image \\( \\phi(H) \\) is still a subgroup of \\( G \\) and is equal to \\( H \\) itself.