ON POSITIVE THEORIES OF GROUPS WITH REGULAR FREE LENGTH FUNCTIONS

DOI10.1142/S0218196707003330zbMath1184.20031OpenAlexW2022032736MaRDI QIDQ5292262

D. E. Serbin, Bilal Khan, Alexei G. Myasnikov

Publication date: 20 June 2007

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196707003330

zbMATH Keywords

groups acting on treesSkolem functionsinfinite wordsequations over groupsLyndon length functionspositive sentencessolvable word problempositive theories of groups

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groups acting on trees (20E08) Quantifier elimination, model completeness, and related topics (03C10)

Related Items

Groups with free regular length functions in $\mathbb{Z}^{n}$ ⋮ Linear groups over general rings. I: Generalities. ⋮ Membership problem in groups acting freely on \(\mathbb N^n\)-trees. ⋮ WORD EQUATIONS OVER GRAPH PRODUCTS ⋮ On Groups in Which Normality Is a Transitive Relation ⋮ ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS ⋮ Hierarchy for groups acting on hyperbolic ℤn-spaces

Cites Work

• Unnamed Item
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
• Implicit function theorem over free groups.
• EXPONENTIAL GROUPS 2: EXTENSIONS OF CENTRALIZERS AND TENSOR COMPLETION OF CSA-GROUPS
• The elementary theory of abelian groups