Prove that $A_n$ is a Normal subgroup of $S_n$?
45277
The alternating group is a normal subgroup of the symmetric group
70373
Intersection of normal subgroups proof
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
75568
Subgroup of index $2$ is Normal
12589
Show that every subgroup of the quaternion group Q is a normal subgroup of Q
99999
A question on identifying normal subgroups of $S_4$
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
102622
K is a subgroup of G. Show that K is not a normal subgroup
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
90332
Prove that that $U(n)$ is an abelian group.
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
22444
Normal subgroups of dihedral groups
151130
When is the product of $n$ subgroups a subgroup?
139096
$|AxA|$ is a constant implies normal subgroup