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Abstract Algebra

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Moderate

Reducible Groups

ABSALG-NVXWCK

We call a group $G$ reducible if $G$ is isomorphic to a product of two non-trivial groups.

Which of the following groups are reducible?

Select ALL that apply.

A

$\mathbb{Z}_8$

B

$S_3$

C

$\mathbb{Z}_2\times \mathbb{Z}_4$

D

$\mathbb{Z}_12$

E

$D_4$