query: Are all simple finite groups unique?
positive_passages.docid: 150760
positive_passages.text: Are there any distinct finite simple groups with the same order?
negative_passages.docid: 67973
negative_passages.text: Prove that a finite abelian group is simple if and only if its order is prime.
negative_passages.docid: 49338
negative_passages.text: Is every group a Galois group?
negative_passages.docid: 58694
negative_passages.text: Which non-abelian finite groups have the property that every subgroup is normal?
negative_passages.docid: 2254
negative_passages.text: Finite group with isomorphic normal subgroups and non-isomorphic quotients?
negative_passages.docid: 102903
negative_passages.text: Python: Uniqueness for list of lists
negative_passages.docid: 106660
negative_passages.text: Every subgroup of the integers has finite index
negative_passages.docid: 40513
negative_passages.text: A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
negative_passages.docid: 78553
negative_passages.text: A simple finite group $G$ with $n$ p-Sylows is isomorphic to a subgroup of $\mathbb A_n$
negative_passages.docid: 81406
negative_passages.text: Does every set have a group structure?
negative_passages.docid: 151193
negative_passages.text: Simple subgroup of Symmetric Group
negative_passages.docid: 6189
negative_passages.text: Examples of infinite groups such that all their respective elements are of finite order.
negative_passages.docid: 51145
negative_passages.text: Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
negative_passages.docid: 39100
negative_passages.text: Exercise from Serre's "Trees" - prove that a given group is trivial
negative_passages.docid: 80381
negative_passages.text: Groups with "few" subgroups
negative_passages.docid: 4184
negative_passages.text: Is Lagrange's theorem the most basic result in finite group theory?
negative_passages.docid: 121423
negative_passages.text: Prove that every element of a finite group has an order