- #1
kathrynag
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Homework Statement
1. Let G and H be finite groups and let a: G → H be a group homomorphism. Show
that if |G| is a prime, then a is either one-to-one or the trivial homomorphism.
2. Let G and H be finite groups and let a : G → H be a group homomorphism. Show
that if |H| is a prime, then a is either onto or the trivial homomorphism.
Homework Equations
The Attempt at a Solution
1. We know a(b)a(c)=a(bc) since it is a homomorphism
order is prime.
need to show a(x1)=a(x2) implies x1=x2. I'm confused on how the oder being prime plays into this.