query: Show that $S_n \cong A_n \rtimes C_2$
positive_passages.docid: 24561
positive_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 115876
negative_passages.text: $D_6 \cong D_3\times \mathbb Z_2$
negative_passages.docid: 55902
negative_passages.text: Show $R[x]/(x)\cong R$
negative_passages.docid: 104274
negative_passages.text: Express $C$ interms of the sets $A_n$
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 15276
negative_passages.text: $G \times H \cong G \times K$ , then $ K \cong H$
negative_passages.docid: 7575
negative_passages.text: Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
negative_passages.docid: 58863
negative_passages.text: Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
negative_passages.docid: 98284
negative_passages.text: show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
negative_passages.docid: 122581
negative_passages.text: Prove or disprove that $G_1/H_1 \cong G_2/H_2$
negative_passages.docid: 78263
negative_passages.text: Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
negative_passages.docid: 70861
negative_passages.text: $\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
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: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
negative_passages.docid: 52642
negative_passages.text: Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$