query: Group of even order must contain $a:a=a^{-1}$ $ (a\not = e)$
positive_passages.docid: 26398
positive_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 140673
negative_passages.text: how to find the order of an element in a quotient group
negative_passages.docid: 85579
negative_passages.text: $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
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: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 30676
negative_passages.text: $G'$ and the product of all the elements in an odd order group
negative_passages.docid: 52357
negative_passages.text: If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
negative_passages.docid: 150585
negative_passages.text: Group with $a=a^{-1}$ for all $a\in G$ is abelian
negative_passages.docid: 145127
negative_passages.text: For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
negative_passages.docid: 133762
negative_passages.text: A set which satisfies all conditions for a Group except associativity
negative_passages.docid: 15210
negative_passages.text: Group of order 6 proof
negative_passages.docid: 34972
negative_passages.text: order of non abelian group can't be what?
negative_passages.docid: 151029
negative_passages.text: The number of non normal subgroups of a group cannot be $1$?
negative_passages.docid: 131306
negative_passages.text: Prove that a group of order $2^5 \cdot 7^5$ is not simple
negative_passages.docid: 114590
negative_passages.text: Prove that any finite group $G$ of even order contains an element of order $2.$
negative_passages.docid: 5069
negative_passages.text: $GL_n(\mathbb F_q)$ has an element of order $q^n-1$
negative_passages.docid: 62208
negative_passages.text: If $A$ is a non-empty set, then $A \notin A$