On the existence of kappa-existentially closed groups

Kaya B., Kegel O. H., Kuzucuoglu M.

ARCHIV DER MATHEMATIK, cilt.111, ss.225-229, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 111
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00013-018-1213-x
  • Dergi Adı: ARCHIV DER MATHEMATIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.225-229
  • Anahtar Kelimeler: Existentially closed groups, Infinite symmetric groups, Homogeneous groups
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinality κ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists no κ-existentially closed group of cardinality κ for singular κ. Assuming the generalized continuum hypothesis, we completely determine the cardinals κ ≤ λ for which a κ-existentially closed group of cardinality λ exists