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)
This property modifier is idempotent and a property is a fixed-point, or equivalently, an image of this if and only if it is a:t.i. subgroup property
The right transiter is an operator from the subgroup property space to itself, defined as follows. The right transiter of a subgroup property is the maximum among all subgroup properties for which the following holds:
where denotes the composition operator on subgroup properties.
Definition with symbols
The right transiter of a subgroup property is the property defined by the following criterion:
A subgroup in a group is said to have if and only if whenever has property as a subgroup of , also has property in .
We denote the right transiter of a property as .
In terms of the residual operator
The right transiter of a property is its right residual by itself, with respect to the composition operator.
A general notion of right transiter can be given for any associative quantalic binary operator on a property space. The generic notion inherits many of the nice behaviours from this special case.
Effect on subgroup metaproperties
If satisfies the intermediate subgroup condition, so does the right transiter of .
Computing the right transiter
In the function restriction formalism
If a subgroup property can be expressed by a function restriction formal expression , thne we can do the following: