If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
65613
$G$ is a finite group and $T$ an automorphism of $G$ such that $T$ sends more than $\frac{3}{4}|G|$ elements to their inverse.
156319
Show that a group with $|G| = 33$ contains an element of order $3$
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
66510
A group is abelian if and only if the center of the group is all the group
117815
Non-abelian group $G$ satisfying $(a \cdot b)^i=a^i \cdot b^i,$ for two consecutive integers.
24966
Converse of Lagrange's theorem for abelian groups
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
3838
If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian?
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
71232
if $A$ is Abelian group , $B$ is subgroup of $A$ , Is $B \times A/B \cong A$?
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
13631
Showing group with $p^2$ elements is Abelian
157841
Existence of a non-abelian group of order $p^n$.
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
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.
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n