Let $p, q$ be prime numbers.

What is the degree of field extension of $\mathbb{F}_{p\ ^q} / \mathbb{F}_p$

I have no idea on this but if I had to guess I would say $q$ ?

Any help or insight is deeply appreciated.

  • $\begingroup$ Iteratively construct a basis to show that $\mathbb{F}_{p^q}$ is a $q$-dimensional $\mathbb{F}_p$-vector space. $\endgroup$ – reuns Sep 7 '17 at 5:05
  • 5
    $\begingroup$ How many elements are there in an $n$-dimensional vector space over $\Bbb{F}_p$? $\endgroup$ – Jyrki Lahtonen Sep 7 '17 at 5:55

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