query: Symmetric Group $S_n$ is Generated by Consecutive Transpositions
positive_passages.docid: 148413
positive_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: 87823
negative_passages.text: GAP: how to work with elements of the group ring of the symmetric group $\mathbb{C}[S_k]$?
negative_passages.docid: 157806
negative_passages.text: Order of a element on a Symmetric Group
negative_passages.docid: 96169
negative_passages.text: $n$ divides a product of $n$ consecutive integers (by $n$ divides one of them)
negative_passages.docid: 15202
negative_passages.text: the root of $N$th transpose matrix
negative_passages.docid: 8627
negative_passages.text: Number of equivalence classes of $w \times h$ matrices under switching rows and columns
negative_passages.docid: 122504
negative_passages.text: Factorisations of permutations
negative_passages.docid: 14383
negative_passages.text: Order of Permutation : If $\tau \in S_n$ has order $m$, then $\sigma \tau\sigma^{-1}$ has also order $m$.
negative_passages.docid: 131594
negative_passages.text: Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
negative_passages.docid: 26572
negative_passages.text: Does the Symmetric difference operator define a group on the powerset of a set?
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 72853
negative_passages.text: What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
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: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 117178
negative_passages.text: Cyclic group generators
negative_passages.docid: 55493
negative_passages.text: Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
negative_passages.docid: 31347
negative_passages.text: $A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?