Intersection-transiter

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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 property


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


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 p to the property of being a subgroup whose intersection with any subgroup having property p, also has property p.

Definition with symbols

Let p be a subgroup property. The intersection transiter operator of p is defined as the following property q: a subgroup H has property q in G if and only if for every subgroup K with property p in G, H \cap K also has property p in G.