Groups, Languages, Algorithms.

Intro -- Contents -- Preface -- Formal languages and their application to combinatorial group theory -- 1. Introduction -- 2. Notation and definitions -- 3. Regular languages -- 4. Rational sets -- 5. Context free languages -- 7. Other language classes -- References -- Regular free length functions on Lyndon's free Z[t]-group FZ[t] -- 1. Introduction -- 2. Preliminaries -- 3. A-words -- 4. A free Lyndon length function on CDR(A, X) -- 5. Lyndon's Exponentiation -- 6. Extensions of centralizers -- 7. Embedding of Fz[t] into CDR(Z[t], X) -- 8. Algorithmic problems for FZ[t] -- References -- A-free groups and tree-free groups -- Effective JSJ decompositions -- Introduction -- 1. Preliminaries -- 2. Splittings -- 3. Algorithms over fully residually free groups -- 4. Generalized equations over free groups -- 5. Elimination process: construction of T(Ω) -- 6. Elimination process: periodic structures -- 7. Elimination process: splittings of coordinate groups -- 8. Structure of solutions, the solution tree Tsol(Ω, A) -- 9. Maximal standard quotients and canonical embeddings of F-groups -- 10. Effective free decompositions -- 11. Homomorphisms of finitely generated groups into fully residually free groups -- 12. Free Lyndon length functions on NTQ groups. -- 13. Effective construction of JSJ decompositions of groups from F. -- 14. Homomorphisms into NTQ groups -- 15. Some applications to equations in F-groups -- References -- Algebraic geometry over free groups: Lifting solutions into generic points -- Introduction -- 1. Scheme of the proof -- 2. Elementary properties of liftings -- 3. Cut equations -- 4. Basic automorphisms of orientable quadratic equations -- 5. Generic solutions of orientable quadratic equations -- 6. Small cancellation solutions of standard orientable equations -- 7. Implicit function theorem for quadratic equations.

8. Implicit function theorem for NTQ systems -- 9. Groups that are elementary equivalent to a free group -- References -- Divisibility theory and complexity of algorithms for free partially commutative groups -- 1. Introduction -- 2. Free partially commutative groups -- 3. Divisibility Theory -- 4. Normal forms arising from H N N extensions -- 5. Conjugacy problem -- 6. Complexity of algorithms: some estimates -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.