query: Find the order of $8/9, 14/5,48/28$ in the additive group of $\mathbb{Q}/\mathbb{Z}$
positive_passages.docid: 140673
positive_passages.text: how to find the order of an element in a quotient group
negative_passages.docid: 85106
negative_passages.text: Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
negative_passages.docid: 1576
negative_passages.text: Finding the elements in the group of units of the ring of integers modulo n that are their own inverse.
negative_passages.docid: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 5089
negative_passages.text: An element of a group has the same order as its inverse
negative_passages.docid: 157496
negative_passages.text: Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
negative_passages.docid: 39642
negative_passages.text: Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 63798
negative_passages.text: How can you show there are only 2 nonabelian groups of order 8?
negative_passages.docid: 47824
negative_passages.text: Calculation of subgroups of $(Z_{12}, +)$
negative_passages.docid: 58673
negative_passages.text: Elements of order 5 in $S_7$, odd permutations of order 4 in $S_4$, and find a specific permutation in $S_7$
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$
negative_passages.docid: 117468
negative_passages.text: $o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
negative_passages.docid: 130826
negative_passages.text: Computing class group of $\mathbb Q(\sqrt{6})$
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 33300
negative_passages.text: Showing order of $Z (G) =1$ or $pq$
negative_passages.docid: 51697
negative_passages.text: Additive group contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$