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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s00233-012-9379-1
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.59-66
  • Çukurova University Affiliated: Yes

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 .