query: A question about the orders of the elements of a group
positive_passages.docid: 145127
positive_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: 53357
negative_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 98734
negative_passages.text: Order of a product of elements in a generic group
negative_passages.docid: 107010
negative_passages.text: How many elements of order $k$ are in $S_n$?
negative_passages.docid: 62035
negative_passages.text: Order of automorphism group of cyclic group
negative_passages.docid: 140673
negative_passages.text: how to find the order of an element in a quotient group
negative_passages.docid: 26398
negative_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: 128692
negative_passages.text: Example of an infinite group where every element except identity has order 2
negative_passages.docid: 55719
negative_passages.text: Order of general- and special linear groups over finite fields.
negative_passages.docid: 157582
negative_passages.text: Inverse of $ab$ and its order in a group with relations $a^2=e=b^6$ and $ab=b^4a$
negative_passages.docid: 2731
negative_passages.text: Groups of even order have an element whose order is 2.
negative_passages.docid: 8434
negative_passages.text: Order of $\mathbb{Z}[i]/(1+i)$
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: 113357
negative_passages.text: Groups of order $pqr$ and their normal subgroups
negative_passages.docid: 29051
negative_passages.text: If I know the order of every element in a group, do I know the group?
negative_passages.docid: 112974
negative_passages.text: The $h-$th power of every element in a finite group of order $h$ is the identity element of the group