# Intersection-transiter

From Groupprops

Template:TransiterThis article defines a subgroup property modifier (a unary subgroup property operator) -- viz an operator that takes as input a subgroup property and outputs a subgroup propertyView a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Symbol-free definition

The intersection transiter operator is a map from the subgroup property space to the subgroup property space, that acts as transiter for the commutative associative binary property operator namely the intersection operator. The intersection transiter takes a subgroup property to the property of being a subgroup whose intersection with any subgroup having property , also has property .

### Definition with symbols

Let be a subgroup property. The intersection transiter operator of is defined as the following property : a subgroup has property in if and only if for every subgroup with property in , also has property in .