Can $gHg^{-1} \subseteq H$ but $gHg^{-1} \neq H$
137563
Can a left coset be strictly contained in a right coset?
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
42355
Double check $G\sim H$ iff $G≈H$
75254
Properties possessed by $H , G/H$ but not G
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
140962
Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.
31846
Does $\neg(x > y)$ imply that $y \geq x$?
35188
Counterexample: $G \times K \cong H \times K \implies G \cong H$
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?
113925
Normal Subgroup Counterexample
126065
Example $g\circ f=id_A$ but $f\circ g\neq id_B$
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
151047
a non trivial example: $G/H$ is isomorphic to $G$