For a group $G$, show the relation $x\sim y$ defined by $\exists a(y=axa^{-1})$ is an equivalence relation on $G$.
84397
$x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
27366
Prove that $g$ is tangent to the graph of $f$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
23517
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
150857
Equivalence relations on S given no relation?
101543
Let $A$ be a group, where $a^2=1$, a belongs to $A$. Prove that this group is commutative.
20736
Prove the relation $R$ in $N \times N$ defined by $(a,b) \simeq (c,d)$ iff $ad=bc$ is an equivalence relation.
136883
The class of equivalence.
90584
Show set of affine transformations is a group
98630
For all $x,y\in\mathbb{R}$ define that $x\equiv y$ if $x^{2}=y^{2} $; prove $\equiv$ is an equivalence relation.
85713
Showing Parallelism is an equivalence relation in $\Bbb R ^2$
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
79933
Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group.
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
151047
a non trivial example: $G/H$ is isomorphic to $G$
104977
How to calculate equivalence relations