# Automorph-join-closed subnormal of normal implies conjugate-join-closed subnormal

From Groupprops

This article describes a computation relating the result of the Composition operator (?) on two known subgroup properties (i.e., Automorph-join-closed subnormal subgroup (?) and Normal subgroup (?)), to another known subgroup property (i.e., Conjugate-join-closed subnormal subgroup (?))

View a complete list of composition computations

## Statement

### Statement with symbols

If is an automorph-join-closed subnormal subgroup of and is a normal subgroup of , then is a conjugate-join-closed subnormal subgroup of .

## Related facts

- Left residual of conjugate-join-closed subnormal by normal equals automorph-join-closed subnormal
- Finite-automorph-join-closed subnormal of normal implies finite-conjugate-join-closed subnormal
- Join-transitively subnormal of normal implies finite-conjugate-join-closed subnormal
- 3-subnormal implies finite-conjugate-join-closed subnormal

## Proof

**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]