Characterizations of the Solvable Radical
| dc.creator | Flavell, Paul | |
| dc.creator | Guest, Simon | |
| dc.creator | Guralnick, Robert | |
| dc.date | 2009-02-10 | |
| dc.date.accessioned | 2026-07-07T12:39:54Z | |
| dc.date.available | 2026-07-07T12:39:54Z | |
| dc.description | We prove that there exists a constant $k$ with the property: if $\calC$ is a conjugacy class of a finite group $G$ such that every $k$ elements of $\calC$\ generate a solvable subgroup then $\calC$ generates a solvable subgroup. In particular, using the Classification of Finite Simple Groups, we show that we can take $k=4$. We also present proofs that do not use the Classification theorem. The most direct proof gives a value of $k=10$. By lengthening one of our arguments slightly, we obtain a value of $k=7$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0902.1668 | |
| dc.identifier | http://arxiv.org/abs/0902.1668 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219280 | |
| dc.subject | Group Theory | |
| dc.subject | 20F14; 20D10 | |
| dc.title | Characterizations of the Solvable Radical | |
| dc.type | text |