Question

a) Define a map  from a binary structure to the binary structure , where  is the usual multiplication,...

a) Define a map  from a binary structure to the binary structure , where  is the usual multiplication, by .

(i) Show that  is one-to-one and onto.

(ii) Give a precise formulation of  such that  is an isomophism.

b) Let be a group isomorphism. Prove that  is also a group isomorphism.

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