Group of Order less than 6 is Abelian

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All groups with less than $6$ elements are abelian.


Let $G$ be a non-abelian group.

From Non-Abelian Group has Order Greater than 4, the order of $G$ must be at least $5$.

But $5$ is a prime number.

By Prime Group is Cyclic it follows that a group of order $5$ is cyclic.

By Cyclic Group is Abelian this group is abelian.

Hence the result.


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