query: If $G=S_4, N=\{e;(1,2)(3,4);(1,3)(2,4);(1,4)(2,3)\}$ show that $N\lhd G$
positive_passages.docid: 80186
positive_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 96329
negative_passages.text: Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
negative_passages.docid: 105910
negative_passages.text: How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
negative_passages.docid: 6115
negative_passages.text: Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
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: 104855
negative_passages.text: Prove that $N \subset Z(G)$
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 35800
negative_passages.text: If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
negative_passages.docid: 154878
negative_passages.text: Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
negative_passages.docid: 151727
negative_passages.text: If $|G/H|=4$ then $G$ is union of three proper subgroups
negative_passages.docid: 109109
negative_passages.text: Show that $E(XE[X|G])=E[(E[X|G)^2]$
negative_passages.docid: 65744
negative_passages.text: How can I Prove that H=G or K=G
negative_passages.docid: 77969
negative_passages.text: Question about proof for $S_4 \cong V_4 \rtimes S_3$
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 99694
negative_passages.text: Number of subgroups of $S_4$
negative_passages.docid: 88262
negative_passages.text: How to enumerate subgroups of each order of $S_4$ by hand
negative_passages.docid: 50525
negative_passages.text: Prove that $(n, n, n-1, n-1, \ldots , 4, 4, 3, 3, 2, 2, 1, 1)$ is a graphic!