GAP:IsCharacteristicInParent

This article is about a GAP function.

This GAP function takes as input a group. See more functions like this.
This GAP function outputs a Boolean variable, i.e., it returns either true or false. View other GAP functions with Boolean output

Using this GAP function requires the loading of the following package: sonata

Definition

Function type

IsCharacteristicInParent is a GAP function that takes as input an argument representing a group, and outputs a Boolean answer (true/false).

Behavior

The function is rare in that it depends not just on the isomorphism class of the group provided but the context in which the group was defined. Specifically, it invokes GAP's Parent attribute/function to determine the parent group in which the given group resides, and then determines whether the given group is characteristic in its parent.

Output	Meaning	Comment
`true`	the group is characteristic in its parent	Any group defined directly (Rather than through some intermediate group) will be equal to its parent, so `true` will be returned.
`false`	the group is not characteristic in its parent

To interpret this function, it may be useful to first determine whether the input group equals its own parent. This can be done by the Parent function:

G = Parent(G);

Package requirements

This function requires the Sonata package. If the package is present but not loaded, it can be loaded by the command:

LoadPackage("sonata");

Related functions

Parent: Outputs the parent group for a given group
IsNormal
IsCharacteristic