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May 3, 2017 at 2:15 vote accept Lucas
May 3, 2017 at 1:58 history edited R. van Dobben de Bruyn CC BY-SA 3.0
Remark turns out unnecessary by comment of OP.
May 3, 2017 at 1:42 comment added Lucas Thanks, this is exactly the lemma I was looking for. Actually this works for me, since the article I'm studying is about the existence of a normal basis that the element $a$ such that $\lbrace \sigma(a) \rbrace$ spans $\mathbb{F}_{q^n}$ as a $\mathbb{F}_{q}$-vector space is also a primitive element of $\mathbb{F}_{q^n}$, so, using the normal basis theorem is allowed. Thank you, anyway.
May 3, 2017 at 1:15 history edited R. van Dobben de Bruyn CC BY-SA 3.0
added 310 characters in body
May 3, 2017 at 1:08 history answered R. van Dobben de Bruyn CC BY-SA 3.0