Order of any element divides the order of the group proof
122125
Order of group element divides order of finite group
119808
Proving that $n$-cycle has order $n$
146969
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
92750
Groups where all elements are order 3
150156
Proving that $S_n$ has order $n!$
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
102634
Order of the Rubik's cube group
5089
An element of a group has the same order as its inverse
128692
Example of an infinite group where every element except identity has order 2
121423
Prove that every element of a finite group has an order
138279
Multiplicative order and powers
33300
Showing order of $Z (G) =1$ or $pq$
98734
Order of a product of elements in a generic group
30676
$G'$ and the product of all the elements in an odd order group
61550
Existence of elements of order $p^k$ in a finite group
56492
Does the order of $f(x)$ divide the order of $x$ if $f$ is a group homomorphism?