Generating sets of finite singular transformation semigroups

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

SEMIGROUP FORUM, cilt.86, sa.1, ss.59-66, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 86 Sayı: 1
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s00233-012-9379-1
  • Dergi Adı: SEMIGROUP FORUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.59-66
  • Çukurova Üniversitesi Adresli: Evet

Özet

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 .