Quantifying the Residual Properties of Gamma-Limit Groups
| Autor: | Solie, Brent B. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Brent B. Solie, Int. J. Algebra Comput., 24, 207 (2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S021819671450012X |
| Popis: | Let Gamma be a fixed hyperbolic group. The Gamma-limit groups of Sela are exactly the finitely generated, fully residually Gamma groups. We give a new invariant of Gamma-limit groups called Gamma-discriminating complexity and show that the Gamma-discriminating complexity of any Gamma-limit group is asymptotically dominated by a polynomial. Our proof relies on an embedding theorem of Kharlampovich-Myasnikov which states that a Gamma-limit group embeds in an iterated extension of centralizers over Gamma. The result then follows from our proof that if G is an iterated extension of centralizers over Gamma, the G-discriminating complexity of a rank n extension of a cyclic centralizer of G is asymptotically dominated by a polynomial of degree n. Comment: 22 pages, 6 figures |
| Databáze: | arXiv |
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