Finite or infinite order of elements in a group
8742
Examples and further results about the order of the product of two elements in a group
36882
Two finite abelian groups with the same number of elements of any order are isomorphic
61550
Existence of elements of order $p^k$ in a finite group
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
134376
Let $G$ be a nonabelian group. Let $a \in G$ have order $4$ and let $b \in G$ have order $3$. Then the order of the element $ab$ in $G$
142718
How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
152904
Groups with Same Number Of Elements and Subgroups
31687
Classification of groups of order 30
124224
How many groups of order $n$ with center {e} exist?
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
56607
gcd and order of elements of group
5089
An element of a group has the same order as its inverse
84132
Number of preimages of a group element under a homomorphism.
18881
Number of elements of order $7$ in a group
107010
How many elements of order $k$ are in $S_n$?
79380
How to find the order of a group generated by two elements?
98734
Order of a product of elements in a generic group