Prove that every permutation is the product of disjoint cycles
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
89659
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
75227
If $S=\{1,2,\dots,n\}$ and $P_n(k)$ be the number of permutations of $S$ having $k$ fixed points, then $\sum_{k=0}^nk.P_{n}(k)=n!$
153721
Conjugating a permutation
15452
Proving determinant product rule combinatorially
114796
Direct proof that the product of odd integers is odd
13734
Show that every group of prime order is cyclic
114752
Number of permutations of a specific cycle decomposition
87756
Order of a particular given permutation = LCM(order of all disjoint cycles) ?
96585
Sums and permutation
31347
$A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
16476
Order of the product of two commuting elements with coprime orders in a group.
81231
Count the permutations which are products of exactly two disjoint cycles.
19026
What do all the $k$-cycles in $S_n$ generate?
24212
proving how many permutations exist.
4555
How to write permutations as product of disjoint cycles and transpositions
23544
Complete induction proof that every $n > 1$ can be written as a product of primes