query: order of finit group which has even elements
positive_passages.docid: 26398
positive_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 115746
negative_passages.text: Find the order of a subgroup of $S_5$ generated by two elements
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: 112165
negative_passages.text: Classification of groups of order 12
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: 157806
negative_passages.text: Order of a element on a Symmetric Group
negative_passages.docid: 9393
negative_passages.text: Order of elements is lcm-closed in abelian groups
negative_passages.docid: 81543
negative_passages.text: Finite abelian group contains an element with order equal to the lcm of the orders of its elements
negative_passages.docid: 158282
negative_passages.text: Finite order of an element $f(g)$ of a homomorphism $f$
negative_passages.docid: 53409
negative_passages.text: Show group of order $4n + 2$ has a subgroup of index 2.
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 35660
negative_passages.text: Elements of order 2 in $D_{2n}$
negative_passages.docid: 122970
negative_passages.text: A question on $p$-groups, and order of its commutator subgroup.
negative_passages.docid: 7973
negative_passages.text: Groups of order $pq$ have a proper normal subgroup
negative_passages.docid: 6189
negative_passages.text: Examples of infinite groups such that all their respective elements are of finite order.
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: 48393
negative_passages.text: Abelian groups of order n.