P-group

definitionp-groups

Definition

For finite group $(G,\cdot )$, and prime $p\ge 2$. We say $(G,\cdot )$ is a p-group if every $g\in G$ has order $p^k$ for some $k$. Equivalently, if $G$ is commutative, then $G=G[p]$.

Examples

See

• Proof of P-group Theorem (1)
• Proof of P-group Theorem (2)