query: Every nontrivial subgroup $H$ of $S_9$ containing some odd permutation contains a transposition.
positive_passages.docid: 143293
positive_passages.text: Does every non-trivial subgroup of $S_9$ containing an odd permutation necessarily contain a transposition?
negative_passages.docid: 96680
negative_passages.text: Generators of symmetric group $S_n$
negative_passages.docid: 37331
negative_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 89474
negative_passages.text: every permutation is either even or odd,but not both
negative_passages.docid: 116786
negative_passages.text: normal subgroups of Alternating group
negative_passages.docid: 142413
negative_passages.text: Normal Subgroups of $SU(n)$
negative_passages.docid: 151619
negative_passages.text: A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
negative_passages.docid: 68317
negative_passages.text: Conjugacy class of $G$ splitting as Conjugacy class of $H\unlhd G$
negative_passages.docid: 109245
negative_passages.text: α² is a cycle if and only if s is odd
negative_passages.docid: 83837
negative_passages.text: Odd/Even Permutations
negative_passages.docid: 99999
negative_passages.text: A question on identifying normal subgroups of $S_4$
negative_passages.docid: 153921
negative_passages.text: Infinite nilpotent group, any normal subgroup intersects the center nontrivially
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: 108691
negative_passages.text: Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
negative_passages.docid: 103538
negative_passages.text: Partitions of $n$ into distinct odd and even parts proof
negative_passages.docid: 142739
negative_passages.text: Nonempty subset H of group G is subgroup iff $ab^{-1} \in H $ for any $a,b \in H$
negative_passages.docid: 128300
negative_passages.text: Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.