On $k$-free-like groups
| dc.creator | Olshanskii, A. Yu. | |
| dc.creator | Sapir, M. V. | |
| dc.date | 2008-11-11 | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:24Z | |
| dc.date.available | 2026-07-07T10:17:24Z | |
| dc.description | A $k$-free like group is a $k$-generated group $G$ with a sequence of $k$-element generating sets $Z_n$ such that the girth of $G$ relative to $Z_n$ is unbounded and the Cheeger constant of $G$ relative to $Z_n$ is bounded away from 0. By a recent result of Benjamini-Nachmias-Peres, this implies that the critical bond percolation probability of the Cayley graph of $G$ relative to $Z_n$ tends to $1/(2k-1)$ as $n\to \infty$. Answering a question of Benjamini, we construct many non-free groups that are $k$-free like for all sufficiently large $k$. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0811.1607 | |
| dc.identifier | http://arxiv.org/abs/0811.1607 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173841 | |
| dc.subject | Group Theory | |
| dc.subject | Probability | |
| dc.title | On $k$-free-like groups | |
| dc.type | text |