Finite-conjugate-join-closed subnormal subgroup

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Definition

A subgroup of a group is termed finite-conjugate-join-closed subnormal if the join of finitely many conjugate subgroups to it is subnormal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup
• 2-subnormal subgroup
• 3-subnormal subgroup: For full proof, refer: 3-subnormal implies finite-conjugate-join-closed subnormal
• Join-transitively subnormal subgroup
• Join-transitively subnormal subgroup of normal subgroup: For full proof, refer: Join-transitively subnormal of normal implies finite-conjugate-join-closed subnormal

Weaker properties

• Subnormal subgroup