GENERATING SETS OF FINITE TRANSFORMATION SEMIGROUPS PK (n, r) AND K (n, r)

摘要

Let P-n and T-n be the partial transformation and the full transformation semigroups on the set {1, ..., n}, respectively. In this paper we find necessary and sufficient conditions for any set of partial transformations of height r in the subsemigroup PK(n, r) = {alpha is an element of P-n : vertical bar im(alpha)vertical bar <= r} of P-n to be a (minimal) generating set of PK(n, r); and similarly, for any set of full transformations of height r in the subsemigroup K(n, r) = {alpha is an element of T-n : vertical bar im(alpha)vertical bar <= r} of T-n to be a (minimal) generating set of K(n, r) for 2 <= r <= n-1.