Are all finite groups isomorphic to multiplicative group of a ring
61391
Which finite groups are the group of units of some ring?
65968
Prove that any two cyclic groups of the same order are isomorphic?
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
152603
Group isomorphic to its automorphism group
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
22604
Can $R \times R$ be isomorphic to $R$ as rings?
8623
Finite subgroups of the multiplicative group of a field are cyclic
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
61732
Prove any group with 3 elements is isomorphic to $\mathbb{Z}_3$
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
78553
A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$