Subgroup whose join with any distinct conjugate is the whole group

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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VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A subgroup of a group is termed a subgroup whose join with any distinct conjugate is the whole group if its join with any of its conjugate subgroups other than itself is the whole group.

Relation with other properties

Stronger properties

• Normal subgroup
• Maximal subgroup

Weaker properties

• Pronormal subgroup: For full proof, refer: Join with any distinct conjugate is the whole group implies pronormal
• Self-conjugate-permutable subgroup
• Weakly pronormal subgroup