Every element of a group has finite order
39864
Intersections of all subgroups is a nontrivial subgroup, so every element has finite order.
152904
Groups with Same Number Of Elements and Subgroups
152604
For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
157806
Order of a element on a Symmetric Group
114187
In a finite cyclic group, the generator has the order of the group
61550
Existence of elements of order $p^k$ in a finite group
8742
Examples and further results about the order of the product of two elements in a group
30676
$G'$ and the product of all the elements in an odd order group
13734
Show that every group of prime order is cyclic
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
6189
Examples of infinite groups such that all their respective elements are of finite order.
28676
Is a finite group uniquely determined by the orders of its elements?
55719
Order of general- and special linear groups over finite fields.
13355
Product of elements of a finite abelian group
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
47478
Show that any cyclic group of even order has exactly one element of order $2$
134676
Number of elements of order $p$ is a multiple of $p-1$ (finite group).