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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]
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
- 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.
- 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.