Abstract Algebra

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Moderate

Maximum Order in Finite Abelian Groups

ABSALG-8WOB0V

Suppose that $G$ is an Abelian group of order $16$ with an element of order $8$ and (at least) two elements of order $2$.

Determine $G$ up to isomorphism.

A

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

B

$\mathbb{Z}_8\times \mathbb{Z}_2$

C

$\mathbb{Z}_{16}$

D

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