p-Groups

# p-Groups

Definition: Let $p$ be a prime. A $p$-Group is a group of order $p^k$ for some $k \in \mathbb{N}$. |

For example a $2$-group is any group of order $2$, $4$, $8$, $16$, etc… A $3$-group is any group of order $3$, $9$, $27$, $81$, etc…

More specifically, the cyclic group of order $p$, $\mathbb{Z}_p \cong \mathbb{Z}/p\mathbb{Z}$ is a $p$-group for any prime $p$.