query: Find all subgroups of $(\Bbb Z,+)$
positive_passages.docid: 156941
positive_passages.text: Subgroups of $\mathbb{Z}$
negative_passages.docid: 137691
negative_passages.text: What are the self-normalizing subgroups of $S_n$?
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.
negative_passages.docid: 3317
negative_passages.text: Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
negative_passages.docid: 61226
negative_passages.text: Group Structure on $\Bbb R$
negative_passages.docid: 10816
negative_passages.text: Infinitely generated subgroup of a finitely one (weird)
negative_passages.docid: 119360
negative_passages.text: Find all subrings of $\mathbb{Z}^2$
negative_passages.docid: 84658
negative_passages.text: What is the number of distinct subgroups of the automorphism group of $\mathbf{F}_{3^{100}}$?
negative_passages.docid: 152825
negative_passages.text: what are all the open subgroups of $(\mathbb{R},+)$
negative_passages.docid: 106277
negative_passages.text: Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
negative_passages.docid: 34067
negative_passages.text: Is there a general formula for finding all subgroups of dihedral groups?
negative_passages.docid: 18343
negative_passages.text: Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$
negative_passages.docid: 75670
negative_passages.text: Questions around the number of subgroups of a $p$-group
negative_passages.docid: 105322
negative_passages.text: Computing the quotient of SL(2,Z) by its commutator subgroup
negative_passages.docid: 2767
negative_passages.text: Subgroups of the Klein-4 Group
negative_passages.docid: 139451
negative_passages.text: Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
negative_passages.docid: 142938
negative_passages.text: Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$