This 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 propertyTemplate:Transiter
View a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)
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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 .