Permute and conjugate: the conjugacy problem in relatively hyperbolic groups
| Autor: | Andrew W. Sale, Yago Antolín |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems 20F65 20F10 20F67 General Mathematics Conjugacy problem 010102 general mathematics Group Theory (math.GR) 0102 computer and information sciences Function (mathematics) Length function 01 natural sciences Relatively hyperbolic group Mathematics::Group Theory Permutation Conjugacy class 010201 computation theory & mathematics Bounded function FOS: Mathematics 0101 mathematics Constant (mathematics) Mathematics - Group Theory Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society. 48:657-675 |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms/bdw028 |
| Popis: | Modelled on efficient algorithms for solving the conjugacy problem in hyperbolic groups, we define and study the permutation conjugacy length function. This function estimates the length of a short conjugator between words $u$ and $v$, up to taking cyclic permutations. This function might be bounded by a constant, even in the case when the standard conjugacy length function is unbounded. We give applications to the complexity of the conjugacy problem, estimating conjugacy growth rates, and languages. Our main result states that for a relatively hyperbolic group, the permutation conjugacy length function is bounded by the permutation conjugacy length function of the parabolic subgroups. 18 pages, 8 figures |
| Databáze: | OpenAIRE |
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