Let $p$ be a prime and let $F$ be a field with $p^k$ elements and $K$ a subfield. Show that $Gal(F : K)$ is a cyclic group of order $[F : K]$.
75828
Compute Galois group of $\mathbb F_q/\mathbb F_p$
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
84789
Order of products of elements in a finite Abelian group
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
56439
$f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$?
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
4996
Proving $Gal(K/\mathbb{Q})$ is $D_4$.
78696
Galois group of the product of two fields being the product of Galois groups?
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
55719
Order of general- and special linear groups over finite fields.
114187
In a finite cyclic group, the generator has the order of the group
158282
Finite order of an element $f(g)$ of a homomorphism $f$
15387
Order of $GL(n, \mathbb Z_p)$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
50785
Galois group of $x^4-5$
110390
Order of group $GL_{2}\left( \mathbb{F}_{p}\right) $