Order of Finite Abelian Group with p+ Order p Elements is Divisible by p^2/Examples
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Examples of Order of Finite Abelian Group with $p+$ Order $p$ Elements is Divisible by $p^2$
Order $3$
Let $G$ be a finite abelian group whose identity is $e$.
Let $G$ have more than $2$ elements of order $3$.
Then:
- $9 \divides \order G$
where:
- $\divides$ denotes divisibility
- $\order G$ denotes the order of $G$.