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# Group of Given Order: Properties of a Group of Order $9$

ABSALG-NH1OP4

Which of the following are properties of every group $G$ of order $9$?

Select ALL that apply.

A

$G$ is cyclic.

B

$G$ is abelian.

C

$G$ is simple.

D

There is exactly one other isomorphism class of groups of order $9$ not containing $G$.

E

Either $G$ is cyclic or $G$ is not abelian.