Showing that the groups (Q,+) and (Q⁺,*) are not isomorphic
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
107511
If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
156549
Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
129239
Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
120155
How to show that this group presentation is isomorphic to dihedral group?
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
47239
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
14895
Reference for the subgroup structure of $\rm{PSL}_2(q)$
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$