Combing nilpotent and polycyclic groups
| dc.creator | Gilman, Robert H. | |
| dc.creator | Holt, Derek F. | |
| dc.creator | Rees, Sarah | |
| dc.date | 1999-01-21 | |
| dc.date.accessioned | 2026-07-07T05:27:36Z | |
| dc.date.available | 2026-07-07T05:27:36Z | |
| dc.description | A combing is a set of normal forms for a finitely generated group. This article investigates the language-theoretic and geometric properties of combings for nilpotent and polycyclic groups. It is shown that a finitely generated class 2 nilpotent group with cyclic commutator subgroup is real-time combable, as are also all 2 or 3-generated class 2 nilpotent groups, and groups in certain families of nilpotent groups, e.g. the finitely generated Heisenberg groups, groups of unipotent matrices over the integers and the free class 2 nilpotent groups. Further it is shown that any polycyclic-by-finite group embeds in a real-time combable group. All the combings constructed in the article are boundedly asynchronous, and those for nilpotent-by-finite groups have polynomially bounded length functions, of degree equal to the nilpotency class, c. This result verifies a polynomial upper bound on the Dehn functions of those groups of degree c+1. | |
| dc.description | To appear in the International Journal of Algebra and Computation | |
| dc.identifier | https://arxiv.org/abs/math/9901088 | |
| dc.identifier | http://arxiv.org/abs/math/9901088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77980 | |
| dc.subject | Group Theory | |
| dc.subject | 20F10, 20-04, 68Q40, secondary: 03D40 | |
| dc.title | Combing nilpotent and polycyclic groups | |
| dc.type | text |