m 2QLSclqmxs00_xCY2BdP9GyckMTuBLEbP13BYbElutzjcm5QM2Tg/formResponseLet (G1, -) and (G2, *) be two groups and o G1 G2 be an isomorphism. ThenG2 might be abelian even if G1 is abelianG2 might not be abelian even if G1 is abelian.G2 is abelian if and only if 61 is cyclic.G2 is abelian if G1 is abelian.

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

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

Section3.2: Properties Of Group Elements

Problem 32E: Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.

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m 2
QLSclqmxs00_xCY2BdP9GyckMTuBLEbP13BYbElutzjcm5QM2Tg/formResponse
Let (G1, -) and (G2, *) be two groups and o G1 G2 be an isomorphism. Then
G2 might be abelian even if G1 is abelian
G2 might not be abelian even if G1 is abelian.
G2 is abelian if and only if 61 is cyclic.
G2 is abelian if G1 is abelian.

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