Let (G1, •) and (G2 , *) be two groups and p : G1→ G2 be an isomorphism. Then * G2 might not be abelian even if G1 is abelian. G2 is abelian if and only if G1 is cyclic. G2 might be abelian even if G1 is abelian G2 is abelian if G1 is abelian.

Let (G1, •) and (G2 , ) be two groups and p : G1→ G2 be an isomorphism. Then G2 might not be abelian even if G1 is abelian. G2 is abelian if and only if G1 is cyclic. G2 might be abelian even if G1 is abelian G2 is abelian if G1 is abelian.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 33E: Suppose that G and H are isomorphic groups. Prove that G is abelian if and only if H is abelian.

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Question

Let (G1, •) and (G2 , *) be two groups
and p: G1→ G2 be an isomorphism.
>
Then *
G2 might not be abelian even if G1 is
abelian.
G2 is abelian if and only if G1 is cyclic.
G2 might be abelian even if G1 is
abelian
G2 is abelian if G1 is abelian.

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