query: Why should the intersection of two normal subgroups be trivial.
positive_passages.docid: 27215
positive_passages.text: Intersection of the $p$-sylow and $q$-sylow subgroups of group $G$
negative_passages.docid: 80186
negative_passages.text: How to show that $K\leq S_4$ is a normal subgroup?
negative_passages.docid: 14255
negative_passages.text: Commutator subgroup and cyclic normal subgroup
negative_passages.docid: 2174
negative_passages.text: Proving that HK is a subgroup when K is normal
negative_passages.docid: 20386
negative_passages.text: Any subgroup of index $p$ in a $p$-group is normal.
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: 72150
negative_passages.text: Union of the conjugates of a proper subgroup
negative_passages.docid: 47731
negative_passages.text: Intersection of all $p$-Sylow subgroups is normal
negative_passages.docid: 125244
negative_passages.text: Equivalent definitions of normal subgroups
negative_passages.docid: 122266
negative_passages.text: equivalent definition of normal subgroup
negative_passages.docid: 97928
negative_passages.text: Normal subgroup of a normal subgroup
negative_passages.docid: 129753
negative_passages.text: Prove that a subgroup which contains half of all elements is a normal subgroup.
negative_passages.docid: 139096
negative_passages.text: $|AxA|$ is a constant implies normal subgroup
negative_passages.docid: 144788
negative_passages.text: Cosets of a subgroup do not overlap
negative_passages.docid: 99999
negative_passages.text: A question on identifying normal subgroups of $S_4$
negative_passages.docid: 99114
negative_passages.text: Subgroups of index 3 are normal
negative_passages.docid: 49122
negative_passages.text: Why commutator subgroup is normal to G?