Complete first-order theories of some classical matrix groups over algebraic integers

DOI10.1016/j.jalgebra.2021.04.015OpenAlexW3158199928MaRDI QIDQ2029249

Mahmood Sohrabi, Alexei G. Myasnikov

Publication date: 3 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2021.04.015

zbMATH Keywords

general linear groupspecial linear groupelementary equivalencebi-interpretabilityabelian deformation

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Model-theoretic algebra (03C60)

Cites Work

• Unnamed Item
• Polycyclic-by-finite groups and first-order sentences
• Groups elementarily equivalent to a free 2-nilpotent group of finite rank.
• Groups elementarily equivalent to a free nilpotent group of finite rank
• Quasi finitely axiomatizable totally categorical theories
• The model theory of unitriangular groups
• First order rigidity of non-uniform higher rank arithmetic groups
• Bi-interpretability and QFA structures: study of some soluble groups and commutative rings. (Bi-interprétabilité et structures QFA : étude de groupes résolubles et des anneaux commutatifs
• Bounded Elementary Generation of SL n (O)
• The Undecidability of Algebraic Rings and Fields
• Elementary equivalence of profinite groups
• Describing Groups
• The Logical Complexity of Finitely Generated Commutative Rings
• Quasi-finitely axiomatizable nilpotent groups
• The elementary theory of abelian groups