Let 
be a number
field and let 
be an order in 
.
Then the set of equivalence classes of invertible
fractional ideals of 
forms a multiplicative Abelian group called the Picard group of 
.
If 
is a maximal order, i.e., the ring of
integers of 
,
then every fractional ideal of 
is invertible and the Picard group of 
is the class group of 
. The order of the Picard group of 
is sometimes called the class number
of 
. If 
is maximal, then the order of the Picard group is equal to
the class number of 
.
