GAP:IsTGroup

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

Definition

Function type

This function takes as input a group and outputs a boolean variable (true/false).

Behavior

The behavior is as follows:

• If the group is a T-group, i.e., if every normal subgroup of a normal subgroup is normal, then the function returns true.
• If the group is not a T-group, i.e., if there exists a normal subgroup of a normal subgroup that is not normal, then the function returns false.

Typical use

The typical use is as follows:

IsTGroup(group);

Related functions

• GAP:IsTransitiveWithBigGroup: A general function to test whether a given subgroup property is transitive relative to a particular big group.
• GAP:IsTransitiveInAllSubgroupsOfGroup: A general function to test whether a given subgroup property is transitive relative to all subgroups of a particular big group.
• GAP:IsTStarGroup: Tests whether a group is a T*-group.
• GAP:IsPTGroup

Method

Code

IsTGroup := function(G)
         return(ForAll(NormalSubgroups(G),H -> ForAll(NormalSubgroups(H), K -> IsNormal(G,K))));
end;;