# Intermediately characteristic of transfer-closed characteristic implies intermediately characteristic

From Groupprops

This article describes a computation relating the result of the Composition operator (?) on two known subgroup properties (i.e., Intermediately characteristic subgroup (?) and Transfer-closed characteristic subgroup (?)), to another known subgroup property (i.e., Intermediately characteristic subgroup (?))

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## Statement

### Property-theoretic statement

If denotes the composition operator, we have:

Intermediately characteristic transfer-closed characteristic Intermediately characteristic

### Verbal statement

Any intermediately characteristic subgroup of a transfer-closed characteristic subgroup is intermediately characteristic.