Normal subgroups, Group order, Automorphisms

Question

I am a beginner at Mathematica and have a few problems.

1. Find all normal subgroups of the Alternating Group A[4].
2. Find the order of a group Aut(U[8]).
3. Find the group Aut(S[3]).

I've been trying to solve these problems, but I don't really know how to do it. In second I wrote:

G1 = Automorphisms[U[8]]

GroupOrder[G1]

and Mathematica says

"GroupOrder::grp: "Groupoid[{1,3,5,7},Mod[#1\ #2,8]&] is not a valid group." "

Thanks for any help.

Answer 1

Check out the guide/GroupTheory in the help system. You will want to use AlternatingGroup[], SymmetricGroup[], GroupOrder[], GroupGenerators[] and you may find GroupMultiplicationTable[] and CayleyGraph[] helpful.