Transfer condition operator preserves transitivity

This article gives the statement, and possibly proof, of a subgroup metaproperty (i.e., Transitive subgroup property (?)) satisfying a subgroup metametaproperty (i.e., Transfer condition operator-preserved subgroup metaproperty (?))
View all subgroup metametaproperty satisfactions $|$ View all subgroup metametaproperty dissatisfactions

Statement

Suppose $p$ is a Transitive subgroup property (?). If $T$ denotes the Transfer condition operator (?), the property $T(p)$ is also a transitive subgroup property.

Related facts

• Subhomomorphism relation between transfer condition operator and composition operator
• Transfer condition is composition-closed