Groups, languages, algorithms : AMS-ASL Joint Special Session on Interactions between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland / Alexandre V. Borovik, editor.

Format:

Book

Conference/Event

Contributor:

Borovik, Alexandre V., editor.

Conference Name:

AMS-ASL Joint Special Session on Interactions between Logic, Group Theory, and Computer Science (2003 : Baltimore, Maryland), issuing body.

Series:

Contemporary mathematics (American Mathematical Society) ; v. 378.

Contemporary mathematics, 0271-4132 ; 378

Language:

English

Subjects (All):

Group theory--Congresses.

Group theory.

Finite groups--Congresses.

Finite groups.

Infinite groups--Congresses.

Infinite groups.

Physical Description:

1 online resource (360 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2005]

Language Note:

English

Contents:

""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(â??)""; ""6. Elimination process: periodic structures""; ""7. Elimination process: splittings of coordinate groups""; ""8. Structure of solutions, the solution tree Tsol(â??, 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""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-7968-5

0-8218-3618-8