# 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.

$\blacksquare$