On the probability of satisfying a word in a group
| dc.creator | Abert, Miklos | |
| dc.date | 2005-04-15 | |
| dc.date | 2005-05-03 | |
| dc.date.accessioned | 2026-07-07T05:19:08Z | |
| dc.date.available | 2026-07-07T05:19:08Z | |
| dc.description | We show that for any finite group $G$ and for any $d$ there exists a word $w\in F_{d}$ such that a $d$-tuple in $G$ satisfies $w$ if and only if it generates a solvable subgroup. In particular, if $G$ itself is not solvable, then it cannot be obtained as a quotient of the one relator group $F_{d}/<w>$. As a corollary, the probability that a word is satisfied in a fixed non-solvable group can be made arbitrarily small, answering a question of Alon Amit. | |
| dc.description | Added content. A more general theorem is proved | |
| dc.identifier | https://arxiv.org/abs/math/0504312 | |
| dc.identifier | http://arxiv.org/abs/math/0504312 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74906 | |
| dc.subject | Group Theory | |
| dc.title | On the probability of satisfying a word in a group | |
| dc.type | text |