Join-transiter

From Groupprops
Jump to: navigation, search
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

Let p be a subgroup property. Then the join-transiter of p is the property of being a subgroup such that its join with any subgroup having property p again has property p in the whole group.

Definition with symbols

Let p be a subgroup property. Then the join-transiter of p is the property q such that: A subgroup H has property q in G if and only if whenever K \le G has property p, <H,K> has property p in G.