GAP:IsCompleteGroup

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

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

Behavior

The function behaves as follows:

• If the group is a complete group, i.e., it is a centerless group and every automorphism of it is inner, the function returns true.
• If the group is not a complete group, the function returns false.

Method

Code

IsCompleteGroup := function(G)
        local K, H;
        K := AutomorphismGroup(G);
        return (K = InnerAutomorphismsAutomorphismGroup(K) and IsTrivial(Center\
(G)));
end;;