For an abelian group, is the order of a+b the lowest common multiple of orders a+b
41731
Question about the order of the product of two elements in an abelian group
37061
The order of $ab$ when $a,b$ commute
88344
Order of a group and subsequent subgroups
63499
Groups of prime squared order
8434
Order of $\mathbb{Z}[i]/(1+i)$
26398
Group of even order contains an element of order 2
8742
Examples and further results about the order of the product of two elements in a group
126893
A group of order 2p (p prime) and other conditions - prove abelian.
131946
Order of an Element Under a Homomorphism
5089
An element of a group has the same order as its inverse
124309
$g\in G$ maximal order in $G$ abelian then $G=\left\oplus H$
157806
Order of a element on a Symmetric Group
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
141458
How many subgroups or order 8 an abelian Group of order 72 can have
83654
Order of an element in a finite cyclic group
84789
Order of products of elements in a finite Abelian group
87756
Order of a particular given permutation = LCM(order of all disjoint cycles) ?