A problem about a abelian and normal subgroup
11003
Proving that $G/N$ is an abelian group
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
141265
Finding a normal and not normal subgroup of $S_3$
37971
Prove that the center of a group is a normal subgroup
113925
Normal Subgroup Counterexample
111375
Normality of subgroups and Sylow groups under homomorphisms...
102622
K is a subgroup of G. Show that K is not a normal subgroup
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
123610
How to show that the commutator subgroup is a normal subgroup
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
94999
A subgroup with an index of 2 is normal to the group.
14255
Commutator subgroup and cyclic normal subgroup
152630
showing that a group of order 45 is abelian
101360
Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian?
129830
A group with no proper non-trivial subgroups
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.