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Contemporary Abstract Algebra

21/09/2020 Client: user_3wd25t Deadline: 2 Day

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)

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