On omega-categorical groups and rings of finite burden

Frank Olaf Wagner (1) , Jan Dobrowolski (2)

1 AGL - Algèbre, géométrie, logique
2 Instytut Matematyczny

An ω-categorical group of finite burden is virtually finite-by-abelian; an ω-categorical ring of finite burden is virtually finite-by-null; an ω-categorical NTP2 ring is virtually nilpotent.

Mots clés: finite burden; ω-categorical; group; ring; virtually abelian; virtually null

Domaines: Logique [math.LO]; Théorie des groupes [math.GR]

Frank Olaf Wagner, Jan Dobrowolski. On omega-categorical groups and rings of finite burden. Israel Journal of Mathematics, 2020, 236, pp.801-839. ⟨10.1007/s11856-020-1989-9⟩. ⟨hal-01822386v5⟩