Property $$P_{naive}$$ P naive for acylindrically hyperbolic groups
| Autor: | Carolyn R. Abbott, François Dahmani |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Normal subgroup
Mathematics::Functional Analysis Hyperbolic group High Energy Physics::Lattice General Mathematics High Energy Physics::Phenomenology 010102 general mathematics 01 natural sciences Nonlinear Sciences::Chaotic Dynamics Combinatorics Mathematics::Group Theory Finite collection 0103 physical sciences Ping pong 010307 mathematical physics 0101 mathematics Element (category theory) Mathematics |
| Zdroj: | Mathematische Zeitschrift. 291:555-568 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-018-2094-1 |
| Popis: | We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the $$P_{naive}$$ property: for any finite collection of elements $$h_1, \dots , h_k$$ , there exists another element $$\gamma \ne 1$$ such that for all i, $$\langle h_i, \gamma \rangle = \langle h_i \rangle * \langle \gamma \rangle $$ . We also show that if a collection of subgroups $$H_1, \dots , H_k$$ is a hyperbolically embedded collection, then there is $$\gamma \ne 1$$ such that for all i, $$\langle H_i, \gamma \rangle = H_i * \langle \gamma \rangle $$ . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink