Subgroup whose normal core is fully invariant

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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 of a group is termed a subgroup whose normal core is fully invariant if its normal core is a fully invariant subgroup.

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
Endomorph-dominating subgroup				|FULL LIST, MORE INFO
Sylow subgroup	$p$-subgroup of finite group whose index is relatively prime to $p$			|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Core-characteristic subgroup	normal core is characteristic			|FULL LIST, MORE INFO