Cosets form a group if normal subgroup
5024
Why do we define quotient groups for normal subgroups only?
37971
Prove that the center of a group is a normal subgroup
117479
Mutual set of representatives for left and right cosets: what about infinite groups?
51359
Prove that every subgroup of an abelian group is a normal subgroup.
14301
Union of subgroups is a subgroup if and only if one subgroup is a subset of the other
99999
A question on identifying normal subgroups of $S_4$
113925
Normal Subgroup Counterexample
3462
Proving a set of automorphisms of a group is a group under composition
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
80186
How to show that $K\leq S_4$ is a normal subgroup?
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
124237
Group equals union of three subgroups
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$