query: Subgroups of the simple groups
positive_passages.docid: 25421
positive_passages.text: Simple or not simple Groups
negative_passages.docid: 27780
negative_passages.text: Subgroup which is generated by odd elements
negative_passages.docid: 64408
negative_passages.text: Subgroup of $\mathbb{Q}$ with finite index
negative_passages.docid: 131516
negative_passages.text: Subgroup generated by n-th powers of elements
negative_passages.docid: 27215
negative_passages.text: Intersection of the $p$-sylow and $q$-sylow subgroups of group $G$
negative_passages.docid: 95229
negative_passages.text: Qualifying Exam Question On Elementary Group Theory
negative_passages.docid: 23941
negative_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 157145
negative_passages.text: Subgroup of $S_8$ isomorphic to $G$
negative_passages.docid: 7640
negative_passages.text: Exactly one nontrivial proper subgroup
negative_passages.docid: 44165
negative_passages.text: the image of normal subgroups
negative_passages.docid: 114431
negative_passages.text: Monoids and Subgroups
negative_passages.docid: 2767
negative_passages.text: Subgroups of the Klein-4 Group
negative_passages.docid: 124237
negative_passages.text: Group equals union of three subgroups
negative_passages.docid: 99694
negative_passages.text: Number of subgroups of $S_4$
negative_passages.docid: 27507
negative_passages.text: Subgroups of Symmetric groups isomorphic to dihedral group
negative_passages.docid: 28181
negative_passages.text: Sylow subgroups of $S_3$ and $S_4$
negative_passages.docid: 88344
negative_passages.text: Order of a group and subsequent subgroups