On the proof that, if $(xy)^2=(yx)^2$ for all $x$ and $y$ in a group, then $xy^2=y^2x$ for all $x$ and $y$
9110
Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.
65319
For all $x,y∈\Bbb{R}$ define that $ x\equiv y$ if$ x^2=y^2$
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
68422
Understanding Lagrange's Theorem (Group Theory)
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
92057
Prove that for every odd integer n, there is a group...
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
92873
To prove in a Group Left identity and left inverse implies right identity and right inverse
24966
Converse of Lagrange's theorem for abelian groups
13631
Showing group with $p^2$ elements is Abelian
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
145397
How to prove that for every $i$, $a_i = i$
16948
Need help with a proof that if $xy=0$ then $x=0$ or $y=0$