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Abstract Algebra

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Moderate

Searching for Homomorphic Images of the Alternating Group $A_4$

ABSALG-IEU0ZE

Which of the following groups is a homomorphic image of the group $A_4$ (the alternating group on 4 symbols)?

Note that $G$ is a homomorphic image of the group $A_4$ if there exists an onto homomorphism from $A_4\to G$.

A

$\mathbb{Z}_2$

B

$\mathbb{Z}_3$

C

$\mathbb{Z}_4$

D

$S_3$

E

$\mathbb{Z}_5$