Characteristic-isomorph-free subgroup

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Definition

A subgroup of a group is termed characteristic-isomorph-free if it is a characteristic subgroup and there is no characteristic subgroup of the whole group isomorphic to it.

Relation with other properties

Stronger properties

• Isomorph-free subgroup
• Normal-isomorph-free subgroup:For proof of the implication, refer Normal-isomorph-free implies characteristic-isomorph-free and for proof of its strictness (i.e. the reverse implication being false) refer Characteristic-isomorph-free not implies normal-isomorph-free.

Weaker properties

• Characteristic subgroup: For proof of the implication, refer Characteristic-isomorph-free implies characteristic and for proof of its strictness (i.e. the reverse implication being false) refer Characteristic not implies characteristic-isomorph-free.