Does the order of the subgroup generated by two elements divide the product of the element orders?
8742
Examples and further results about the order of the product of two elements in a group
115746
Find the order of a subgroup of $S_5$ generated by two elements
114187
In a finite cyclic group, the generator has the order of the group
131946
Order of an Element Under a Homomorphism
122125
Order of group element divides order of finite group
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
83710
Order of a homomorphism of groups
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
123560
Intuition behind why order of a subgroup divides order of a group.
104080
Group with order $pq$ has subgroups of order $p$ and $q$
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
28676
Is a finite group uniquely determined by the orders of its elements?
140673
how to find the order of an element in a quotient group
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
27780
Subgroup which is generated by odd elements
100061
The Maximum possible order for an element $S_n$
79380
How to find the order of a group generated by two elements?