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  "body": "\n## Example\n\nThe [[Klein four-group|0PMRQJVTME]] is $V = \\{e, a, b, c\\}$, where $a^2 = b^2 = c^2 = e$ and $ab = ba = c$.\nThe group is abelian.\nEach element that is not $e$ has [[order|0JPYSD5E0B]] $2$. Thus each element generates a subgroup with at most $2$ elements.\nNo element generates all $4$ elements, so $V$ is not [[cyclic|0B85Q41RP6]].\n\n## Remarks\n\nThus the converse of the result that cyclic groups are abelian is false.\nUp to isomorphism, $V$ and $\\mathbb{Z}/4\\mathbb{Z}$ are the only groups of order $4$.\n",
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