Contemporary Abstract Algebra

1.Let G be a group.  

Show that the set Aut(G) consisting of all automorphisms of G is a subgroup of Sym(G)

Show that if G is non-abelian, then |Aut(G)|>1.

2.Determine, with justification, the group Aut(Z10) (your answer should include a full table of products). Is it abelian? 

3.Let n≥2. Determine, with justification, the index of On(R) in GLn(R)