If p is a prime positive integer, find all subfields of GF(p)
This question just seems too vague.
2026-03-30 13:43:37.1774878217
If p is a prime positive integer, find all subfields of GF(p)
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Any subfield necessarily contains the multiplicative identity, $1$. Because the characteristic of $\mbox{GF}(p)$ is $p$, we know that $1$ generates an additive subgroup of order $p$, which can only be $\mbox{GF}(p)$ itself. Hence any subfield containing $1$ also contains $\mbox{GF}(p)$. It follows that there are no proper subfields.