let $|S| = 3$. Prove $(P(S),\Delta)$ is not isomorphic to $(\mathbb{Z_8},+)$.
44497
Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
156679
$K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
120183
Prove that $S_3\times\mathbb{Z}_2$ is isomorphic to $D_6$
83919
How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$?
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
125668
A proof that BS(1,2) is not polycyclic
38911
Squares in $\mathbb{Z}_p$ that are not squares in $\mathbb{Z}$
157853
$Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
106091
Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
43462
Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
113359
Proving that $x^2 + 4$ is not divisible by $3$