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 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
