Let (G1, ) and (G2 , *) be two groups andp: G1 G2 be an isomorphism. Then *O G2 might be abelian even if G1 is abelianO G2 is abelian if G1 is abelian.OG2 is abelian if and only if G1 is cyclic.G2 might not be abelian even if G1 isabelian.

given that G1,. and G2,*are two groups and φ:G1→G2 be an isomorphism

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1,) and (G2,*) be two groups and →G2 be an isomorphism. Then *

1,) and (G2,) be two groups and →G2 be an isomorphism. Then

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 *
O G2 might be abelian even if G1 is abelian
O G2 is abelian if G1 is abelian.
OG2 is abelian if and only if G1 is cyclic.
G2 might not be abelian even if G1 is
abelian.

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