query: Are elements in $A_n$ the squares of elements in $S_n$?
positive_passages.docid: 147746
positive_passages.text: Characterisation of the squares of the symmetric group
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: 157840
negative_passages.text: Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
negative_passages.docid: 100061
negative_passages.text: The Maximum possible order for an element $S_n$
negative_passages.docid: 146204
negative_passages.text: Subsets sharing at most $i$ elements
negative_passages.docid: 46355
negative_passages.text: If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
negative_passages.docid: 92672
negative_passages.text: Number of elements which are cubes/higher powers in a finite field.
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: 96123
negative_passages.text: Element of maximal order in alternating group $A_{10}$: how to prove this is it?
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 131516
negative_passages.text: Subgroup generated by n-th powers of elements
negative_passages.docid: 125702
negative_passages.text: There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
negative_passages.docid: 117658
negative_passages.text: A set with n elements has 2^n subsets
negative_passages.docid: 61550
negative_passages.text: Existence of elements of order $p^k$ in a finite group
negative_passages.docid: 72389
negative_passages.text: Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
negative_passages.docid: 5692
negative_passages.text: Proving that there is a perfect square between $n$ and $2n$
negative_passages.docid: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group