query: Let $G ⊂ S_7$ be a subgroup of order 8. Then there exists $i$ such that $\sigma(i)=i.$
positive_passages.docid: 29457
positive_passages.text: Using orbit stabilizer theorem
negative_passages.docid: 15706
negative_passages.text: "Every Group of order $216$ contains a normal subgroup of order $27$ or $9$
negative_passages.docid: 42389
negative_passages.text: If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
negative_passages.docid: 6899
negative_passages.text: $D_8$ as a derived subgroup
negative_passages.docid: 58863
negative_passages.text: Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
negative_passages.docid: 146760
negative_passages.text: Prove that H is a subgroup of G
negative_passages.docid: 3756
negative_passages.text: If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
negative_passages.docid: 133001
negative_passages.text: $G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
negative_passages.docid: 57427
negative_passages.text: Group of order $8p$ is solvable, for any prime $p$
negative_passages.docid: 128834
negative_passages.text: Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
negative_passages.docid: 3317
negative_passages.text: Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 151130
negative_passages.text: When is the product of $n$ subgroups a subgroup?
negative_passages.docid: 107935
negative_passages.text: If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
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: 70001
negative_passages.text: Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
negative_passages.docid: 15526
negative_passages.text: Question on groups of order $pq$