$|G':G''| \le p^2$ implies $G'$ is abelian
90811
If $[G' : G'']\leq p^2$, then $G'$ is abelian.
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
26624
Prove that is group is abelian
57809
For which $n$, $G$ is abelian?
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
138406
If N and every subgroup of N is normal in G then G/N is abelian .
122335
Abelian $p$-group with unique subgroup of index $p$
8602
Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
98647
$G$ is Topological $\implies$ $\pi_1(G,e)$ is Abelian
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
46863
Show that $g$ is injective
90332
Prove that that $U(n)$ is an abelian group.
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
143314
Sylow subgroup of $S_{p^2}$