[GAP Forum] question

[Alexander Konovalov]

On 6 Aug 2008, at 15:42, Elaheh khamseh wrote:

> Can i find the groups have only identity automorphism?

Dear Elaneh Khamseh,

In GAP, for a finite group you can construct its automorphism group
and then you may see if it is trivial or not. For example,

gap> G:=CyclicGroup(3);
<pc group of size 3 with 1 generators>
gap> Size(AutomorphismGroup(G));
2

so here Aut(G) is not trivial.

It is easy to see without GAP that the group of order two has trivial
automorphism group. This can be demonstrated in GAP as below:

gap> G:=CyclicGroup(2);
<pc group of size 2 with 1 generators>
gap> Size(AutomorphismGroup(G));
1

It is an easy exercise to prove that there are no other non-trivial
(finite and infinite) groups with this property.

Hope this helps.

Best wishes,
Alexander