Proving that $V$ and $V^*$ are not naturally isomorphic
54333
In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?
115663
Proving an isomorphism using the isomorphism theorems
150885
$v \otimes v' = v' \otimes v$ implies $v = av'$
52556
Isomorphism of $S^1$.
113261
How to find a vector space V and decompositions $V=A\oplus B = C\oplus D$ with $A$ isomorphic to $C$ but $B$ is not isomorphic to $D?$
96363
How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
67383
Prove that $G'$ is not planar.
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
73248
Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
8694
$A_4$ is not isomorphic to $D_6$
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.