Connection between an order of an element and an order of a group
26398
Group of even order contains an element of order 2
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
41731
Question about the order of the product of two elements in an abelian group
8742
Examples and further results about the order of the product of two elements in a group
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$
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 ?
119758
On the order of elements of $\mathrm{GL}(2,q)$.
93198
The order of a conjugacy class is bounded by the index of the center
39938
Subgroups of a cyclic group and their order.
122959
How is number of conjugacy class related to the order of a group?
84397
$x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
115746
Find the order of a subgroup of $S_5$ generated by two elements
2731
Groups of even order have an element whose order is 2.
44224
Understanding the order() function
30676
$G'$ and the product of all the elements in an odd order group