Galois actions of finitely generated groups rarely have model companions
Bulletin of the London Mathematical Society, cilt.56, sa.2, ss.847-859, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 56 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.1112/blms.12969
- Dergi Adı: Bulletin of the London Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.847-859
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We show that if (Formula presented.) is a finitely generated group such that its profinite completion (Formula presented.) is “far from being projective” (i.e., the kernel of the universal Frattini cover of (Formula presented.) is not a small profinite group), then the class of existentially closed (Formula presented.) -actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is “far from being projective,” the main result of this paper corrects an error in our paper, Beyarslan and Kowalski (Proc. London Math. Soc., (2) 118 (2019), 221–256), by showing the negation of Theorem 3.26 in that paper.