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).
