Finite Abelian groups: G×H≅G×K then H≅K
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
48393
Abelian groups of order n.
130937
Embeddings of finite groups into $\mathrm{GL}_n(\mathbb{Z})$
85222
Direct sum of finitely-many non-abelian groups
1577
Order of nontrivial elements is 2 implies Abelian group
139100
A question on the group algebra $k[G]$ of a finite abelian group
125640
Group of order $p^2$ is abelian.
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
25235
Finite abelian groups - direct sum of cyclic subgroup
13355
Product of elements of a finite abelian group
43750
Subgroups of finite solvable groups. Solvable?
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
30825
Infinite coproduct of abelian groups
18415
Direct sum of Abelian groups and Isomorphism
81354
The product of all the elements of a finite abelian group
108425
Problem on abelian group
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.