Group having no proper isoclinic subgroup

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group is termed a group having no proper isoclinic subgroup if there is no proper subgroup of the group that is isoclinic to the whole group. In other words, no proper subgroup is isoclinic to the whole group as abstract groups, i.e., there exists no isoclinism between the two groups.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Group having no proper cocentral subgroup