query: Show that if a transitive subgroup $G\subset S_n$ of the symmetric group $S_n$ contains a n-1 cycle and transposition,then $G=S_n$.
positive_passages.docid: 35472
positive_passages.text: Transitive subgroup of symmetric group $S_n$ containing an $(n-1)$-cycle and a transposition
negative_passages.docid: 59561
negative_passages.text: Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
negative_passages.docid: 110708
negative_passages.text: On proving that a finitely generated group has a finite number of subgroups with index $n$.
negative_passages.docid: 58108
negative_passages.text: The alternating group is generated by three-cycles
negative_passages.docid: 79055
negative_passages.text: Orders of a symmetric group
negative_passages.docid: 147746
negative_passages.text: Characterisation of the squares of the symmetric group
negative_passages.docid: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?
negative_passages.docid: 31347
negative_passages.text: $A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
negative_passages.docid: 44942
negative_passages.text: A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$
negative_passages.docid: 155372
negative_passages.text: Find the number of permutations in $S_n$ containing fixed elements in one cycle
negative_passages.docid: 152662
negative_passages.text: Proving that any finite cyclic group of order $n$ is isomorphic to $$
negative_passages.docid: 41294
negative_passages.text: Permutation module of $S_n$
negative_passages.docid: 27507
negative_passages.text: Subgroups of Symmetric groups isomorphic to dihedral group
negative_passages.docid: 148413
negative_passages.text: Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
negative_passages.docid: 58863
negative_passages.text: Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
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: 81864
negative_passages.text: Finite group of order $mn$ with $\gcd(m,n) = 1$ .