| Título: | Algorithmic and approximation problems in free constructions |
| Autores: | Lioutikova, Ekaterina. |
| Fecha: | 1999 |
| Publicador: | McGill University |
| Fuente: |
Ver documento |
| Tipo: | Electronic Thesis or Dissertation |
| Tema: | Mathematics. |
| Descripción: | In the first part of this thesis, we introduce a class of groups whose maximal abelian subgroups are either malnormal or modules over a given ring A, and use free constructions to describe explicitly the structure of tensor A-completion for groups from this class. As a corollary, we obtain a description of tensor completion for groups of the form F/ N', in particular, free solvable groups. The tensor completion GQ of a torsion-free hyperbolic group over the field of rational numbers can be similarly described in terms of free constructions. Using this description of G Q, in the second part of this thesis we provide an algorithm that decides whether a finite system of equations over G Q is solvable, and if it is, finds a solution. In the third part of this thesis we study residual properties of Lyndon's group FZx (the free exponential group over the ring of integral polynomials Z[x]), whose structure also involves free constructions. We show that FZx is conjugately residually free, i.e., it is possible to map FZx to a free group preserving the nonconjugacy of two elements. |
| Idioma: | en |
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