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Let G and G' be groups, and 6: G→ G' be a homomorphism. Prove that if |G| is prime, then either (G) is the trivial subgroup of G' or o(G) is isomorphic to G.

Let G and G' be groups, and 6: G→ G' be a homomorphism. Prove that if |G| is prime, then either (G) is the trivial subgroup of G' or o(G) is isomorphic to G.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 28E
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Let G and G' be groups, and o: G → G' be a either (G) is the trivial subgroup of G' or o(G) is isomorphic to G. homomorphism. Prove that if |G| is prime, then
Transcribed Image Text:Let G and G' be groups, and o: G → G' be a either (G) is the trivial subgroup of G' or o(G) is isomorphic to G. homomorphism. Prove that if |G| is prime, then
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