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


AYIK H. , BUGAY L.

COMMUNICATIONS IN ALGEBRA, vol.43, no.2, pp.412-422, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1080/00927872.2013.847947
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.412-422

Abstract

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.