Answered: ) If we have an epimorphism from G to…

) If we have an epimorphism from G to G’, then we know G must be the same or of bigger order than G’. (Can you explain why?)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.6: Homomorphisms

Problem 16E: 16. Suppose that and are groups. If is a homomorphic image of , and is a homomorphic image of ,...

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Question

a.) If we have an epimorphism from G to G’, then we know G must be the same or of bigger order than G’. (Can you explain why?)

b.) If G and G’ are of the same order, it’s pretty easy to get the isomorphism. (Again, can you explain why?)

c.) If the order of G is larger than the order of G’ AND the operation is maintained by this mapping, where do all of the “extra” elements in G have to be mapping?

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