# Finite-conjugate-join-closed subnormal subgroup

From Groupprops

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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 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`