query: Priority of the 3 axioms of groups
positive_passages.docid: 25567
positive_passages.text: Is there any significance in the order in which group axioms are presented?
negative_passages.docid: 1577
negative_passages.text: Order of nontrivial elements is 2 implies Abelian group
negative_passages.docid: 87451
negative_passages.text: Construction of matrices under ZFC axioms
negative_passages.docid: 52451
negative_passages.text: Ordered Triples and Set Theory
negative_passages.docid: 155207
negative_passages.text: Confusion regarding one formulation of the Axiom of Choice.
negative_passages.docid: 13807
negative_passages.text: Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
negative_passages.docid: 2731
negative_passages.text: Groups of even order have an element whose order is 2.
negative_passages.docid: 79055
negative_passages.text: Orders of a symmetric group
negative_passages.docid: 114662
negative_passages.text: Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
negative_passages.docid: 20252
negative_passages.text: The Axiom of Choice and the Cartesian Product.
negative_passages.docid: 130771
negative_passages.text: Sets and the principle of inclusion and exclusion
negative_passages.docid: 123560
negative_passages.text: Intuition behind why order of a subgroup divides order of a group.
negative_passages.docid: 134938
negative_passages.text: Committee combinatorics
negative_passages.docid: 49162
negative_passages.text: Classify all groups with order $pq$, $p$ is not equal to $q$
negative_passages.docid: 130706
negative_passages.text: Group presentations and the Dihedral Group
negative_passages.docid: 142840
negative_passages.text: Open axioms of equality
negative_passages.docid: 29755
negative_passages.text: Power set equivalency of Axiom of Choice