How to prove that order of a field is a power of its characteristic?
3703
Order of finite fields is $p^n$
52614
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
83452
Prove that any conjugate of $a$ has the same order as $a$.
31977
How to prove sum of powers property of roots of unity?
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
155771
Product of degree of two field extensions of prime degree
156859
Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.
7567
Degree of Field Extensions and $F(\alpha)$
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
4401
Constructive proof that algebraic numbers form a field
70776
Characteristic of a field is $0$ or prime
81441
Degree of splitting field divides n!
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
119808
Proving that $n$-cycle has order $n$
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
22995
Let f:G to H be 1-1 homomorphism show that order of f(a) divides the order of G.
119758
On the order of elements of $\mathrm{GL}(2,q)$.