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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.