Prime Groups of Same Order are Isomorphic

Theorem

Two prime groups of the same order are isomorphic to each other.

Proof

Let $G_1$ and $G_2$ be prime groups, both of finite order $p$.

From Prime Group is Cyclic, both $G_1$ and $G_2$ are cyclic.

The result follows directly from Cyclic Groups of Same Order are Isomorphic.

$\blacksquare$

Sources

• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.9$