$GL_n(\mathcal{F})$ is a finite group if and only if $\mathcal{F}$ is finite
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
66510
A group is abelian if and only if the center of the group is all the group
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
64408
Subgroup of $\mathbb{Q}$ with finite index
91085
how to find $|GL_2(F_p)|$
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
128305
$PGL(n, F)=PSL(n, F)$
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
98474
Show the existence of a certain subgroup of F2
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
105610
Normalizer of upper triangular group in ${\rm GL}(n,F)$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements