Lower central and derived series of semi-direct products, and applications to surface braid groups
| Autor: | Carolina de Miranda e Pereiro, John Guaschi |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Universidade Federal do Espirito Santo (UFES) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
MSC Primary: 20F36
20F14 Secondary: 20E26 Algebra and Number Theory Series (mathematics) 010102 general mathematics Braid group Boundary (topology) Central series Surface (topology) 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Combinatorics Nilpotent Product (mathematics) [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences 010307 mathematical physics 0101 mathematics Klein bottle Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra Journal of Pure and Applied Algebra, Elsevier, 2020, 224 (7), pp.106309. ⟨10.1016/j.jpaa.2020.106309⟩ |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2020.106309⟩ |
| Popis: | For an arbitrary semi-direct product, we give a general description of its lower central series and an estimation of its derived series. In the second part of the paper, we study these series for the full braid group B n ( M ) and pure braid group P n ( M ) of a compact surface M, orientable or non-orientable, the aim being to determine the values of n for which B n ( M ) and P n ( M ) are residually nilpotent or residually soluble. We first solve this problem in the case where M is the 2-torus. We then use the results of the first part of the paper to calculate explicitly the lower central series of P n ( K ) , where K is the Klein bottle. Finally, if M is a non-orientable, compact surface without boundary, we determine the values of n for which B n ( M ) is residually nilpotent or residually soluble in the cases that were not already known in the literature. |
| Databáze: | OpenAIRE |
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