1.77: Order
If
G
is a group consisting of a finite number of elements, this number of elements is the
order
of
G
. For example, the point group
m
3
m
has order 48.
For an element
g
of a (not necessarily finite) group
G
, the
order
of
g
is the smallest integer
n
such that
g
n
is the identity element of
G
. If no such integer exists,
g
is of
infinite order
. For example, the rotoinversion
3
has order 6 and a translation has infinite order. An element of order 2 is called an
involution
.