Can every finite index subgroup of $\mathbb{Z}\times\mathbb{Z}$ be written as $\langle n\cdot e_1,m\cdot e_2\rangle$?
74044
Find all subgroups of $\mathbb{Z}\times\mathbb{Z}$.
58925
Order of general linear group of $2 \times 2$ matrices over $\mathbb{Z}_3$
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
98474
Show the existence of a certain subgroup of F2
28210
A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
54082
Group with exactly two subgroups of index 2
145339
Index of the subgroup $\operatorname{Im}(f)$
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
58863
Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
41231
Subgroups of (Z,+) of order n
147968
Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
156909
$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
128989
Is ${\bf Z} \times {\bf Z}$ elementarily equivalent to ${\bf Z}$?
157840
Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?