query: $G$ be a non-nilpotent and supersoluble and 2-maximal subgroup of G permutes with all 3-maximal subgroup of G
positive_passages.docid: 145254
positive_passages.text: $G$ be a non-nilpotent and supersoluble finite group.
negative_passages.docid: 78580
negative_passages.text: Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
negative_passages.docid: 85018
negative_passages.text: When is the automorphism group of the Cayley graph of $G$ just $G$?
negative_passages.docid: 121034
negative_passages.text: Follow-up to question: Aut(G) for G = Klein 4-group is isomorphic to $S_3$
negative_passages.docid: 150207
negative_passages.text: Non isomorphic subgroups of cyclic groups
negative_passages.docid: 91774
negative_passages.text: Existence of group $G$ with $|G|>2$ and automorphism group of odd order
negative_passages.docid: 36147
negative_passages.text: A finite group is nilpotent iff two elements with relatively prime order commute
negative_passages.docid: 58108
negative_passages.text: The alternating group is generated by three-cycles
negative_passages.docid: 114811
negative_passages.text: Characteristic subgroups and automorphisms
negative_passages.docid: 28210
negative_passages.text: A finite group with exactly $2$ conjugacy classes isomorphic to $\mathbb{Z}_2$
negative_passages.docid: 58033
negative_passages.text: $G\times H\cong G$ with $H$ non-trivial
negative_passages.docid: 59902
negative_passages.text: Example of $2$ non-isomorphic groups that have the same quotients
negative_passages.docid: 64269
negative_passages.text: Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
negative_passages.docid: 12455
negative_passages.text: $|G|>2$ implies $G$ has non trivial automorphism
negative_passages.docid: 151699
negative_passages.text: Group of inner automorphisms of a group $G$
negative_passages.docid: 88726
negative_passages.text: Problem about solvable groups
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2