On the Universal Theory of Torsion and Lacunary Hyperbolic Groups

DOI10.1515/GCC.2009.311zbMath1195.03042arXiv0903.3978OpenAlexW2963280708MaRDI QIDQ5189811

Denis V. Osin

Publication date: 11 March 2010

Published in: Groups – Complexity – Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3978

zbMATH Keywords

torsion groupuniversal theorylacunary hyperbolic group

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Periodic groups; locally finite groups (20F50) Model-theoretic algebra (03C60) Decidability of theories and sets of sentences (03B25) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (1)

A topological zero-one law and elementary equivalence of finitely generated groups

Cites Work

• Elementary theory of free non-abelian groups.
• Lacunary hyperbolic groups. With an appendix by Michael Kapovich and Bruce Kleiner.
• Unsolvability of the universal theory of finite groups
• The word problem for the Burnside varieties
• The SQ-universality and residual properties of relatively hyperbolic groups.
• Embedding free Burnside groups in finitely presented groups.
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• A Reduction of the Open Sentence Problem for Finite Groups
• A SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR 2-GROUPS
• ON RESIDUALING HOMOMORPHISMS AND G-SUBGROUPS OF HYPERBOLIC GROUPS
• THE FREE BURNSIDE GROUPS OF SUFFICIENTLY LARGE EXPONENTS
• Hyperbolic groups and their quotients of bounded exponents
• Diophantine geometry over groups VII: The elementary theory of a hyperbolic group

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