query: Prove that $A_n$ is normal in $S_n$
positive_passages.docid: 45277
positive_passages.text: The alternating group is a normal subgroup of the symmetric group
negative_passages.docid: 48607
negative_passages.text: If $A$ is normal and $A$ and $B$ commute, then $A^*$ and $B$ commute
negative_passages.docid: 119118
negative_passages.text: Prove $n\mid \phi(2^n-1)$
negative_passages.docid: 103501
negative_passages.text: Question about a normal equation proof
negative_passages.docid: 11834
negative_passages.text: Prove that $\liminf x_n = -\limsup (-x_n)$
negative_passages.docid: 158082
negative_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 29996
negative_passages.text: Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
negative_passages.docid: 51359
negative_passages.text: Prove that every subgroup of an abelian group is a normal subgroup.
negative_passages.docid: 80186
negative_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 41445
negative_passages.text: Show that the sequence $a_n\leq a_{2n}+a_{2n+1}$ diverges
negative_passages.docid: 150156
negative_passages.text: Proving that $S_n$ has order $n!$
negative_passages.docid: 140400
negative_passages.text: Prove normal matrix is 4th power of some self-adjoint matrix
negative_passages.docid: 110018
negative_passages.text: Conjugacy classes in $A_n$.
negative_passages.docid: 51747
negative_passages.text: Showing that the intersection of all subgroups of order $n$ is normal
negative_passages.docid: 67295
negative_passages.text: Please check my proof for $N$ is infinite
negative_passages.docid: 151520
negative_passages.text: About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
negative_passages.docid: 13742
negative_passages.text: Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.