GAP:IsCompleteGroup

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.

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