Subgroup isoclinic to the whole group
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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]
Definition
A subgroup isoclinic to the whole group is defined as a subgroup such that there is an isoclinism between the subgroup and the whole group. In other words, the whole group and the subgroup are isoclinic groups.
Note that if the whole group is a finite group, this is equivalent to being a cocentral subgroup.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Subgroup isomorphic to the whole group | ||||
| Cocentral subgroup | ||||
| Normal subgroup isoclinic to the whole group |