Centralizer-annihilating endomorphism-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

A subgroup $H$ of a group $G$ is termed a centralizer-annihilating endomorphism-invariant subgroup of $G$ if, for every centralizer-annihilating endomorphism $\sigma$ of $G$, $\sigma (H)$ is contained in $H$. Here, a centralizer-annihilating endomorphism of $G$ with respect to $H$ is an endomorphism whose kernel contains the centralizer $C_{G}(H)$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
fully invariant subgroup				|FULL LIST, MORE INFO
fully normalized potentially fully invariant subgroup		fully normalized and potentially fully invariant implies centralizer-annihilating endomorphism-invariant