Isomorphic finite abelian groups
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
151047
a non trivial example: $G/H$ is isomorphic to $G$
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
5741
Direct product of abelian groups
47539
Find an abelian infinite group such that every proper subgroup is finite
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
142421
Conjugacy Classes in Finite Groups
152954
Extensions of finite cyclic groups
152603
Group isomorphic to its automorphism group
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
61513
Prove that all cyclic groups of the same order are isomorphic
17978
Isomorphism classes of $\mathbb{Z}[i]$ modules.
113259
The confusing nature of direct sum for finite abelian groups
18415
Direct sum of Abelian groups and Isomorphism
86174
Finding an isomorphism between these two finite fields
115973
Computing the number of nonisomorphic finite abelian groups of order $n$