Packing subgroups in solvable groups
| Autor: | Pranab Sardar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Property (philosophy)
Group (mathematics) General Mathematics Geometric Topology (math.GT) Combinatorics Negative - answer Mathematics::Group Theory Mathematics - Geometric Topology Solvable group Locally finite group Retract Bounded function Physical Sciences and Mathematics FOS: Mathematics math.GT Finitely-generated abelian group Mathematics |
| Zdroj: | Sardar, Pranab. (2014). Packing subgroups in solvable groups. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/9mz9g1th |
| Popis: | We show that any subgroup of a (virtually) nilpotent-by-polycyclic group satisfies the bounded packing property of Hruska-Wise. In particular, the same is true about metabelian groups and linear solvable groups. However, we find an example of a finitely generated solvable group of derived length 3 which admits a finitely generated subgroup without the bounded packing property. In this example the subgroup is a metabelian retract also. Thus we obtain a negative answer to Problem 2.27 of Hruska-Wise. On the other hand, we show that polycyclic subgroups of solvable groups satisfy the bounded packing property. 8 pages, no figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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