The
order of an
element a in a
group is the least positive
integer n such
an=e or infinity
if no such
n exists (here
e
is the
identity element of
G).
The order of a group is its number of elements.
If a is an element of a group G then
<a> denotes the cyclic subgroup of G
consisting of all powers {am: m in Z}.
The order of the element a in G is the same as the order of the group <a>.