For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
3907
Abelian quotient group
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
7324
Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$
39895
Showing a free abelian group is generated by its basis
63162
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
138410
Centralizer of $\mathbb{C}[G]$ in $\mathbb{C}[H]$
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
5741
Direct product of abelian groups
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
13355
Product of elements of a finite abelian group
90332
Prove that that $U(n)$ is an abelian group.
13631
Showing group with $p^2$ elements is Abelian
35913
Abelianization of free group is the free abelian group
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
122353
Status of the classification of non-finitely generated abelian groups.
65900
Show that a finite group with certain automorphism is abelian
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian