query: Prove that $S_n$ is isomorphic to a subgroup of $A_{n+2}$
positive_passages.docid: 18141
positive_passages.text: Embedding $S_n$ into $A_{n+2}$
negative_passages.docid: 90437
negative_passages.text: Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 57309
negative_passages.text: Show that the free group on $n$ generators is a finite index subgroup of $F_2$
negative_passages.docid: 66708
negative_passages.text: Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$
negative_passages.docid: 138297
negative_passages.text: Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
negative_passages.docid: 11665
negative_passages.text: Show that $D_{12}$ is isomorphic to $D_6\times C_2$
negative_passages.docid: 101176
negative_passages.text: Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$
negative_passages.docid: 151130
negative_passages.text: When is the product of $n$ subgroups a subgroup?
negative_passages.docid: 36137
negative_passages.text: Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
negative_passages.docid: 29717
negative_passages.text: Not sure how to go about this group theory proof
negative_passages.docid: 37928
negative_passages.text: Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
negative_passages.docid: 74218
negative_passages.text: Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
negative_passages.docid: 7575
negative_passages.text: Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
negative_passages.docid: 130081
negative_passages.text: Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
negative_passages.docid: 40321
negative_passages.text: $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
negative_passages.docid: 149578
negative_passages.text: Subgroups of $(\mathbb Z_n,+)$