There is no proper subgroup of $\mathbb Q$ of finite index
64408
Subgroup of $\mathbb{Q}$ with finite index
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
156941
Subgroups of $\mathbb{Z}$
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
129937
How to prove that $A_5$ has no subgroup of order 30?
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
144582
Index of a subgroup in $SL_2(\mathbb{Z})$
129830
A group with no proper non-trivial subgroups
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
109060
Group containing no subgroup of index 2
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
75828
Compute Galois group of $\mathbb F_q/\mathbb F_p$
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?