The group of all nonsingular 
stochastic matrices
over a field 
. It is denoted 
. If 
is prime and 
is the finite field of order 
, 
is written instead of 
. Particular examples include
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
where 
is an Abelian group, 
are symmetric groups
on 
elements, and 
denotes the semidirect product with 
(Poole 1995).
