# Join-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

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

### Definition with symbols

Let be a subgroup property. Then the join-transiter of is the property such that: A subgroup has property in if and only if whenever has property , has property in .