query: Non-existence of non-abelian simple groups of order $90$ by counting elements
positive_passages.docid: 20944
positive_passages.text: How do I show that every group of order 90 is not simple?
negative_passages.docid: 149030
negative_passages.text: Nonisomorphic groups of order 12.
negative_passages.docid: 59902
negative_passages.text: Example of $2$ non-isomorphic groups that have the same quotients
negative_passages.docid: 91774
negative_passages.text: Existence of group $G$ with $|G|>2$ and automorphism group of odd order
negative_passages.docid: 46940
negative_passages.text: On Groups of Order 315 with a unique sylow 3-subgroup .
negative_passages.docid: 53357
negative_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 129830
negative_passages.text: A group with no proper non-trivial subgroups
negative_passages.docid: 90329
negative_passages.text: Prove there is no simple group of order $729$
negative_passages.docid: 61546
negative_passages.text: Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 141188
negative_passages.text: Groups of order $56$
negative_passages.docid: 151029
negative_passages.text: The number of non normal subgroups of a group cannot be $1$?
negative_passages.docid: 8746
negative_passages.text: Groups of order $pq$ without using Sylow theorems
negative_passages.docid: 49162
negative_passages.text: Classify all groups with order $pq$, $p$ is not equal to $q$
negative_passages.docid: 120557
negative_passages.text: Group of invertible elements of a ring has never order $5$
negative_passages.docid: 88718
negative_passages.text: A group is generated by two elements of order $2$ is infinite and non-abelian
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?