Core-characteristic subgroup

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

Symbol-free definition

A subgroup of a group is termed core-characteristic if its normal core is a characteristic subgroup of the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed core-characteristic if the normal core $H_G$ of $H$ in $G$ is a characteristic subgroup of $G$.

Relation with other properties

Stronger properties

• Characteristic subgroup
• Automorph-conjugate subgroup
• Intersection of automorph-conjugate subgroups
• Core-free subgroup

Conjunction with other properties

Any normal subgroup that is also core-characteristic, is characteristic.

Incomparable properties

• Closure-characteristic subgroup