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


AYIK H. , BUGAY L.

COMMUNICATIONS IN ALGEBRA, cilt.43, ss.412-422, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 43 Konu: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1080/00927872.2013.847947
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Sayfa Sayıları: ss.412-422

Özet

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.