On the palindromic and primitive widths of a free group
| dc.creator | Bardakov, Valery | |
| dc.creator | Shpilrain, Vladimir | |
| dc.creator | Tolstykh, Vladimir | |
| dc.date | 2003-11-16 | |
| dc.date.accessioned | 2026-07-07T05:02:56Z | |
| dc.date.available | 2026-07-07T05:02:56Z | |
| dc.description | Let G be a group and S a subset of G that generates G. For each x in G define the length l_S(x) of x relative to S to be the minimal k such that x is a product of k elements of S. The supremum of the values l_S(x), x \in G, is called the width of G with respect to S. Here we focus on a free group F. The width of F relative to the set of all primitive (respectively palindromic) elements is called the primitive (respectively palindromic) width of F. We prove that for a free group F_n of finite rank n, both widths are infinite. A result of independent interest is that every primitive element of F_2 is a product of at most two palindromes. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311257 | |
| dc.identifier | http://arxiv.org/abs/math/0311257 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69211 | |
| dc.subject | Group Theory | |
| dc.title | On the palindromic and primitive widths of a free group | |
| dc.type | text |