About coset and normal subgroup
7108
Normal subgroup of prime index
27728
Question on a homomorphism of a set G.
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
102622
K is a subgroup of G. Show that K is not a normal subgroup
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
22444
Normal subgroups of dihedral groups
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
58205
$ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
48273
If a maximal subgroup is normal, it has prime index
35602
If a subgroup has smallest prime index, then it is normal
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.