Let φ : G → H be an onto homomorphism.(a) Assume that G is abelian. Does this imply that H is abelian? Whatabout the converse?(b) What if we replaced abelian by cyclic in the above question.
Let φ : G → H be an onto homomorphism.(a) Assume that G is abelian. Does this imply that H is abelian? Whatabout the converse?(b) What if we replaced abelian by cyclic in the above question.
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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Let φ : G → H be an onto homomorphism.
(a) Assume that G is abelian. Does this imply that H is abelian? What
about the converse?
(b) What if we replaced abelian by cyclic in the above question.
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