query: If every nonidentity element in a group is of order $2$, the group is abelian
positive_passages.docid: 20679
positive_passages.text: Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 5089
negative_passages.text: An element of a group has the same order as its inverse
negative_passages.docid: 26624
negative_passages.text: Prove that is group is abelian
negative_passages.docid: 71420
negative_passages.text: Prove that a group is abelian.
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 48393
negative_passages.text: Abelian groups of order n.
negative_passages.docid: 134376
negative_passages.text: Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
negative_passages.docid: 81354
negative_passages.text: The product of all the elements of a finite abelian group
negative_passages.docid: 108310
negative_passages.text: $(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group
negative_passages.docid: 15633
negative_passages.text: If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
negative_passages.docid: 47239
negative_passages.text: For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
negative_passages.docid: 49768
negative_passages.text: If Gal(K,Q) is abelian then |Gal(K,Q)|=n
negative_passages.docid: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 99309
negative_passages.text: Groups of order $n^2$ that have no subgroup of order $n$
negative_passages.docid: 102971
negative_passages.text: Product of all elements of a finite group with an unique element of order 2
negative_passages.docid: 41731
negative_passages.text: Question about the order of the product of two elements in an abelian group