Show that if $|I| > \frac{3}{4}|G|$ then $G$ is abelian.
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
46863
Show that $g$ is injective
3907
Abelian quotient group
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
104855
Prove that $N \subset Z(G)$
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
97565
Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$
98542
Prove that $H$ is a subgroup of an abelian group $G$
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
125640
Group of order $p^2$ is abelian.
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
74964
Showing Galois Group is Abelian