Existentially closed CSA-groups.

DOI10.1016/j.jalgebra.2004.06.007zbMath1080.20026OpenAlexW2067410209MaRDI QIDQ1763914

Eric Jaligot, Abderezak Ould Houcine

Publication date: 22 February 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.06.007

zbMATH Keywords

maximal subgroupsfinitely generated groupssimple groupsfirst-order theoriesmalnormal subgroupsexistentially closed groupsbad groupsconjugately separated Abelian groupsCSA-groups

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Model-theoretic algebra (03C60) Simple groups (20E32) Generators, relations, and presentations of groups (20F05) Residual properties and generalizations; residually finite groups (20E26) Classification theory, stability, and related concepts in model theory (03C45)

Related Items

On superstable CSA-groups ⋮ Independence Property and Hyperbolic Groups ⋮ Groups of Finite Morley Rank with Solvable Local Subgroups ⋮ Strongly indecomposable finite groups. ⋮ Simple groups of Morley rank 3 are algebraic ⋮ Model theoretic connected components of groups ⋮ Superstable subgroups of \(\text{SL}_2(K)\) and \(\text{PSL}_2(K)\). (Sous-groupes superstables de \(\text{SL}_2(K)\) et de \(\text{PSL}_2(K)\)) ⋮ Subgroup theorem for valuated groups and the CSA property. ⋮ Equations in acylindrically hyperbolic groups and verbal closedness

Cites Work

• \(\exists\)-free groups
• Full Frobenius Groups of Finite Morley Rank and the Feit-Thompson Theorem
• Groups of small Morley rank
• EXPONENTIAL GROUPS 2: EXTENSIONS OF CENTRALIZERS AND TENSOR COMPLETION OF CSA-GROUPS
• CSA-groups and separated free constructions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item