Free Version
Difficult

# Group of a Given Order: Identifying a Group of Order $18$

ABSALG-YJ2SKP

Let $G$ be a group of order $18$ with only one subgroup of order $2$.

Which of the following are properties of every such group $G$?

You can assume the following true fact: Every group of order $9$ is abelian.

Select ALL that apply.

A

$G$ is cyclic.

B

$G$ has a normal subgroup of order $2$.

C

$G$ has two normal subgroups of order $9$.

D

$G$ is abelian.