Isomorph-characteristic 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 of a group is termed an isomorph-characteristic subgroup if every subgroup of the group isomorphic to it is a characteristic subgroup of the whole group.

Relation with other properties

Stronger properties

• Isomorph-free subgroup

Weaker properties

• Isomorph-normal subgroup
• Sylow-relatively weakly closed subgroup