Any finite index subgroup of $\mathbb Z_p$ is open
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
46821
Finding roots in $\mathbb{Z}_p$
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
95867
Subgroup of $C^*$ (nonzero complex) with finite index.
47539
Find an abelian infinite group such that every proper subgroup is finite
133770
Subgroups of finite abelian groups.
75068
subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
69820
A nontrivial p-group has nontrivial center
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
17978
Isomorphism classes of $\mathbb{Z}[i]$ modules.
153934
How to prove that a set R\Z is open
122335
Abelian $p$-group with unique subgroup of index $p$
54453
Finite abelian $p$-group with only one subgroup size $p$ is cyclic
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
49666
Generalization of index 2 subgroups are normal