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Suppose H is a subgroup of G such that ϕ(H)=H for all ϕ is an element...

Suppose H is a subgroup of G such that ϕ(H)=H for all ϕ is an element in Aut(G). Prove H is a normal subgroup of G.

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Answer #1

Given:   is a subgroup of .

To prove :   is a normal subgroup of

Proof: Let and

Since the mapping    defined as    is an automorphism

i.e

   and   

  is a normal subgroup of

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