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Abstract Algebra

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Groups of Cube Prime Power Order

ABSALG-UJUGRE

Suppose $G$ is a group of order $p^3$, where $p$ is a prime number.

Which of the following is true about $G$?

Select \textbf{ALL} that apply.

A

$G$ is abelian.

B

$G/Z(G)$ is abelian.

C

$G$ is abelian or $|Z(G)|=p$.

D

$G$ is abelian or $g^p\in Z(G)$ for all $g\in G$.

E

$G/Z(G)$ is cyclic.