Left transiter preserves intersection-closedness

This article gives the statement, and possibly proof, of a subgroup metaproperty (i.e., Intersection-closed subgroup property (?)) satisfying a subgroup metametaproperty (i.e., Left transiter-preserved subgroup metaproperty (?))
View all subgroup metametaproperty satisfactions $|$ View all subgroup metametaproperty dissatisfactions

Statement

Verbal statement

The left transiter of an intersection-closed subgroup property is again an intersection-closed subgroup property.

Related facts

Stronger facts

• Intersection-closedness is left residual-preserved

Related facts

• Left transiter preserves join-closedness
• Left transiter preserves upward-closedness
• Right transiter preserves intermediate subgroup condition
• Right transiter preserves upper join-closedness