Abelian-extensible automorphism-invariant subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

Suppose $G$ is an abelian group and $H$ is a subgroup of $G$. We say that $H$ is an abelian-extensible automorphism-invariant subgroup of $G$ if, for every abelian-extensible automorphism $\sigma$ of $G$, we have $\sigma (H)=H$.

Relation with other properties

Stronger properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Characteristic subgroup of abelian group				|FULL LIST, MORE INFO
Abelian-potentially characteristic subgroup	a characteristic subgroup in some bigger abelian group	abelian-potentially characteristic implies abelian-extensible automorphism-invariant		|FULL LIST, MORE INFO
Subgroup of finite abelian group	subgroup of finite abelian group	(via abelian-potentially characteristic; see finite abelian NPC theorem)		|FULL LIST, MORE INFO

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Subgroup of abelian group