query: No subgroups of $A_{n+1}$ is isomorphic to $S_n$
positive_passages.docid: 131594
positive_passages.text: Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
negative_passages.docid: 108691
negative_passages.text: Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
negative_passages.docid: 51861
negative_passages.text: $S_4$ is not isomorphic to $D_{12}$
negative_passages.docid: 157853
negative_passages.text: $Q_8$ is isomorphic to a subgroup of $S_8$, but not isomorphic to a subgroup of $S_n$ for $n\leq 7$.
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?
negative_passages.docid: 59138
negative_passages.text: Subgroups of $S_4$ isomorpic to $S_2$
negative_passages.docid: 27507
negative_passages.text: Subgroups of Symmetric groups isomorphic to dihedral group
negative_passages.docid: 75012
negative_passages.text: Additive group of rationals has no minimal generating set
negative_passages.docid: 88645
negative_passages.text: Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 18160
negative_passages.text: How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
negative_passages.docid: 70298
negative_passages.text: Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
negative_passages.docid: 144788
negative_passages.text: Cosets of a subgroup do not overlap
negative_passages.docid: 47179
negative_passages.text: Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
negative_passages.docid: 18141
negative_passages.text: Embedding $S_n$ into $A_{n+2}$
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: 142413
negative_passages.text: Normal Subgroups of $SU(n)$
negative_passages.docid: 149578
negative_passages.text: Subgroups of $(\mathbb Z_n,+)$