How does the element of the field $F_{p^4}$ look like? Can I say it will look like $ [\theta , a , a^2 ,...., a^{(p^4 -1)} = 1]$

Question

How does the element of the field $F_{p^4}$ look like?

Can I say it will look like $ [\theta , a , a^2 ,...., a^{(p^4 -1)} = 1]$?

Is there any better way to represent it?

Answer 1

Yes, can say that there is $a \in \mathbb F_{p^4}$ such that $ \mathbb F_{p^4} = \{0 , a , a^2 ,...., a^{(p^4 -1)} = 1\}$ because every finite multiplicative subgroup of a field is cyclic.