Limit groups and automorphisms of κ-existentially closed groups
Journal of Algebra, cilt.666, ss.840-849, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 666
- Basım Tarihi: 2025
- Doi Numarası: 10.1016/j.jalgebra.2024.12.003
- Dergi Adı: Journal of Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.840-849
- Anahtar Kelimeler: Algebraically closed groups, Automorphism groups, Existentially closed groups
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
The structure of automorphism groups of κ-existentially closed groups has been studied by Kaya-Kuzucuoğlu in 2022. It was proved that Aut(G) is the union of subgroups of level preserving automorphisms and |Aut(G)|=2κ whenever κ is an inaccessible cardinal and G is the unique κ-existentially closed group of cardinality κ. The cardinality of the automorphism group of a κ-existentially closed group of cardinality λ>κ is asked in Kourovka Notebook Question 20.40. Here we answer positively the promised case κ=λ namely: If G is a κ-existentially closed group of cardinality κ, then |Aut(G)|=2κ. We also answer Kegel's question on universal groups, namely: For any uncountable cardinal κ, there exist universal groups of cardinality κ.