Question: (a) For a group G and g E G let c : GG be defined by ca(r) =gg for all x G. Prove that

(a) For a group G and g E G let c :

(a) For a group G and g E G let c : GG be defined by ca(r) =gg for all x G. Prove that c, is an isomorphism (i.e. a homomorphism and a bijection). (b) Use your table for the group S, to calculate the normalizer Ng = { S3 | gr=xg} for each element g E Sa (c) Are all of your normalizers in (b) normal?

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