The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n, F). If p is prime and F is the finite field of order q = p^m, S(n, q) is written instead of S(n, F). Particular examples include S(2, 2) | = | Z_2 S(2, 3) | = | S_3 S(2, 4) | = | A_4 S(3, 2) | = | S_4 S(2, 5) | = | Z_4 ×_θ Z_5, where Z_2 is an Abelian group, S_n are symmetric groups on n elements, and ×_θ denotes the semidirect product with θ:Z_4->Aut(Z_5).