What are the uses of homomorphisms and isomorphisms in the study of group theory?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 9E: 9. Find all homomorphic images of the octic group.
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1) What are the uses of homomorphisms and isomorphisms in the study of group theory?

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