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  "body": "\n## Definition\n\nLet $L/K$ be a [[Galois extension|0DS2F7GK05]] with [[Galois group|0XVR72M51M]] $\\Gal(L/K)$.\nThe extension $L/K$ is *cyclic* if $\\Gal(L/K)$ is a [[cyclic group|0B85Q41RP6]].\nIt is *cyclic of degree $n$* if moreover $\\Gal(L/K)$ has order $n$.\n\n## Remarks\n\nExample: let $p$ be a prime, $q$ a power of $p$, and $n \\ge 1$.\nThe extension $\\F_{q^n}/\\F_q$ of finite fields is cyclic of degree $n$, generated by the Frobenius map $x \\mapsto x^q$.\nNon-example: $\\Q(\\sqrt{2}, \\sqrt{3})/\\Q$ is Galois with group $\\Z/2 \\times \\Z/2$.\nEvery element of this group has order at most $2$, while the group has order $4$, so it is not cyclic.\nEvery cyclic extension is an [[abelian extension|EQDEXBWGJH]].\n",
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