Smallest $n$ such that $U(n)$ contains a subgroup isomorphic to $\mathbb Z_5 \oplus \mathbb Z_5$
70904
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
64408
Subgroup of $\mathbb{Q}$ with finite index
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
111375
Normality of subgroups and Sylow groups under homomorphisms...
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
133770
Subgroups of finite abelian groups.
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
12667
How many subgroups of order $n$ does $D_n$ have?
66806
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
149578
Subgroups of $(\mathbb Z_n,+)$
27507
Subgroups of Symmetric groups isomorphic to dihedral group
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.