Cauchy's Lemma (Group Theory)

Theorem
Let $\struct {G, \circ}$ be a group of finite order whose identity is $e$.

Let $p$ be a prime number which divides the order of $G$.

Then $\struct {G, \circ}$ has an element of order $p$.

Also known as
Cauchy's lemma is also known as Cauchy's theorem, but there are also other results with that name.

To distinguish between them, some sources refer to this as Cauchy's group theorem.

's approach directs us to use the name Cauchy's lemma.