Strict dead end elements in free soluble groups
| dc.creator | Guba, Victor | |
| dc.date | 2005-08-22 | |
| dc.date.accessioned | 2026-07-07T05:22:36Z | |
| dc.date.available | 2026-07-07T05:22:36Z | |
| dc.description | Let $G$ be a group generated by a finite set $A$. An element $g\in G$ is a strict dead end of depth $k$ (with respect to $A$) if $|g|>|ga_1|>|ga_1a_2|>...>|ga_1a_2... a_k|$ for any $a_1,a_2, ..., a_k\in A^{\pm1}$ such that the word $a_1a_2... a_k$ is freely irreducible. (Here $|g|$ is the distance from $g$ to the identity in the Cayley graph of $G$.) We show that in finitely generated free soluble groups of degree $d\ge2$ there exist strict dead elements of depth $k=k(d)$, which grows exponentially with respect to $d$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508422 | |
| dc.identifier | http://arxiv.org/abs/math/0508422 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76120 | |
| dc.subject | Group Theory | |
| dc.subject | 20F32; 05C25 | |
| dc.title | Strict dead end elements in free soluble groups | |
| dc.type | text |