Order of a permutation in $S_n$
33216
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.
44480
Let $\sigma :\{1,2,3,4,5\} \rightarrow \{1,2,3,4,5\}$ be permutations such that $ \sigma^{-1}(j) \leq \sigma(j)~\forall j, 1 \leq j \leq 5$.
28266
For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
83837
Odd/Even Permutations
29678
Circular Permutation
133497
Group Membership Test for Permutations
115209
Elementary formula for permutations?
37061
The order of $ab$ when $a,b$ commute
61324
Finding the "square root" of a permutation
53357
Cyclic Group Generators of Order $n$
60416
Finding a permutation, and number of, from powers of the permutation
83654
Order of an element in a finite cyclic group
88344
Order of a group and subsequent subgroups
149609
Conditions on cycle types for permutations to generate $S_n$
73323
Permutations when some objects are alike
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
101719
Finding the n-th lexicographic permutation of a string