Let G and H be finite groups. Prove the following statements. (a) If a: G H is a homomorphism, then |a(G)| divides gcd(|G|, |H|). (b) If |G| and |H| are relatively prime, then there are no homomorphisms from G to H other than the trivial homomorphism.
Let G and H be finite groups. Prove the following statements. (a) If a: G H is a homomorphism, then |a(G)| divides gcd(|G|, |H|). (b) If |G| and |H| are relatively prime, then there are no homomorphisms from G to H other than the trivial homomorphism.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 17E
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