query: intersection of two non empty subgroups of (Q,+) is not equal to {0}
positive_passages.docid: 139451
positive_passages.text: Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
negative_passages.docid: 127996
negative_passages.text: $M_1$ and $M_2$ are subgroups and $M_1/N=M_2/N$. Is $M_1\cong M_2$?
negative_passages.docid: 104080
negative_passages.text: Group with order $pq$ has subgroups of order $p$ and $q$
negative_passages.docid: 120495
negative_passages.text: Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
negative_passages.docid: 45580
negative_passages.text: Intersection of conjugate subgroups is normal
negative_passages.docid: 108049
negative_passages.text: Determining the number of subgroups of $\Bbb Z_{14} \oplus \Bbb Z_{6}$
negative_passages.docid: 57883
negative_passages.text: Example of a Subgroup That Is Not Normal
negative_passages.docid: 142938
negative_passages.text: Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
negative_passages.docid: 64269
negative_passages.text: Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
negative_passages.docid: 157853
negative_passages.text: $Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
negative_passages.docid: 18160
negative_passages.text: How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
negative_passages.docid: 105139
negative_passages.text: Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center
negative_passages.docid: 19720
negative_passages.text: A normal subgroup intersects the center of the $p$-group nontrivially
negative_passages.docid: 74218
negative_passages.text: Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
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: 3317
negative_passages.text: Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
negative_passages.docid: 113925
negative_passages.text: Normal Subgroup Counterexample