How to show that $\langle a \rangle$ is a normal Subgroup of a group $G$
45028
How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
139096
$|AxA|$ is a constant implies normal subgroup
58251
To show every sylow p-subgroup is normal in G
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
78580
Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
28108
Proving the kernel is a normal subgroup.
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
14255
Commutator subgroup and cyclic normal subgroup
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
89215
How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
154398
Show that H is a subgroup of G
80186
How to show that $K\leq S_4$ is a normal subgroup?
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$