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  "body": "\n## Statement\n\nLet $F$ be a [[finite field|08RTDHX1SK]] of order $q$.\nThen the multiplicative group $F^\\times$ is cyclic of order $q - 1$.\n\n## Remarks\n\nThis is the case $G = F^\\times$ of the [[theorem on finite subgroups|0CKGBEJX6B]].\nA generator of $F^\\times$ is a [[primitive element|0YAA9CJQXF]] of $F$.\nFor $F = \\mathbb{Z}/p\\mathbb{Z}$, the statement says that there is a primitive root modulo $p$.\nFor example, $3$ generates $(\\mathbb{Z}/7\\mathbb{Z})^\\times$, with powers $3, 2, 6, 4, 5, 1$.\n\n## Explanations\n\n### L1 human\n\nAll the nonzero elements of a finite field are powers of one element.\nSo multiplication in a finite field is like addition of exponents modulo $q - 1$.\n",
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