Generating sets of finite singular transformation semigroups


AYIK G. , AYIK H. , BUGAY L. , KELEKCI O.

SEMIGROUP FORUM, vol.86, no.1, pp.59-66, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s00233-012-9379-1
  • Title of Journal : SEMIGROUP FORUM
  • Page Numbers: pp.59-66

Abstract

J.M. Howie proved that , the semigroup of all singular mappings of {1,aEuro broken vertical bar,n} into itself, is generated by its idempotents of defect 1 (in J. London Math. Soc. 41, 707-716, 1966). He also proved that if na parts per thousand yen3 then a minimal generating set for contains n(n-1)/2 transformations of defect 1 (in Gomes and Howie, Math. Proc. Camb. Philos. Soc. 101. 395-403, 1987). In this paper we find necessary and sufficient conditions for any set for transformations of defect 1 in to be a (minimal) generating set for .