query: Proving that doesn't exist subgroup H with order 6 in $A_4$
positive_passages.docid: 76943
positive_passages.text: Existence of subgroup of order six in $A_4$
negative_passages.docid: 139451
negative_passages.text: Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
negative_passages.docid: 140334
negative_passages.text: Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
negative_passages.docid: 80849
negative_passages.text: There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
negative_passages.docid: 151029
negative_passages.text: The number of non normal subgroups of a group cannot be $1$?
negative_passages.docid: 75670
negative_passages.text: Questions around the number of subgroups of a $p$-group
negative_passages.docid: 90081
negative_passages.text: problems in group theory
negative_passages.docid: 135465
negative_passages.text: Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
negative_passages.docid: 85011
negative_passages.text: Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
negative_passages.docid: 155054
negative_passages.text: $G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?
negative_passages.docid: 91774
negative_passages.text: Existence of group $G$ with $|G|>2$ and automorphism group of odd order
negative_passages.docid: 7575
negative_passages.text: Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
negative_passages.docid: 49257
negative_passages.text: How to show that Klein four-group is a normal subgroup of the alternating group $A_4$
negative_passages.docid: 28181
negative_passages.text: Sylow subgroups of $S_3$ and $S_4$
negative_passages.docid: 80186
negative_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 74218
negative_passages.text: Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
negative_passages.docid: 103829
negative_passages.text: Find the subgroups of A4