Why can't be ($\mathbb{Z}_5,+) $ isomorphic to $U(R)$ for some rings $R$ where $U(R)$ is the unity groups of $R$?
120557
Group of invertible elements of a ring has never order $5$
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
6385
Minimal counterexamples of the isomorphism problem for integral group rings
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
68728
Why does the natural ring homomorphism induce a surjective group homomorphism of units?
150204
Isomorphisms between the groups $U(10), U(5)$ and $\mathbb{Z}/4\mathbb{Z}$
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
47114
What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings?
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
113512
Characteristic of nonzero commutative rings with unity
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$