query: What is maximal possible order of an element in $S_{10}$ ? Why?
positive_passages.docid: 21568
positive_passages.text: Maximal order of an element in a symmetric group
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 107010
negative_passages.text: How many elements of order $k$ are in $S_n$?
negative_passages.docid: 30172
negative_passages.text: Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10?
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: 26398
negative_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 33216
negative_passages.text: Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
negative_passages.docid: 131163
negative_passages.text: There is a well ordering of the class of all finite sequences of ordinals
negative_passages.docid: 69833
negative_passages.text: Number of elements not equal to their inverses is even number
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
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: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 114662
negative_passages.text: Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
negative_passages.docid: 91557
negative_passages.text: Show that total orders are maximal orders
negative_passages.docid: 158282
negative_passages.text: Finite order of an element $f(g)$ of a homomorphism $f$
negative_passages.docid: 38083
negative_passages.text: Order of conjugate of an element given the order of its conjugate
negative_passages.docid: 50762
negative_passages.text: If $S_n$ has cyclic subgroups of these orders or not?