Cauchy's Group Theorem/Proof 2
< Cauchy's Group Theorem(Redirected from Group has Subgroup of Prime Order if Prime Divides Order/Proof 2)
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Theorem
Let $G$ be a finite group whose identity is $e$.
Let $p$ be a prime number which divides order of $G$.
Then $G$ has a subgroup of order $p$.
Proof
This result follows as a special case of Group has Subgroups of All Prime Power Factors.
$\blacksquare$