Show that if G and H are isomorphic group, then G commutative implies H is commutative also.
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Show that if G and H are isomorphic group, then G commutative implies H is commutative also.
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- 16. Suppose that is an abelian group with respect to addition, with identity element Define a multiplication in by for all . Show that forms a ring with respect to these operations.Prove that if is an isomorphism from the group G to the group G, then 1 is an isomorphism from G to G.Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.