A commutator description of the solvable radical of a finite group
| dc.creator | Gordeev, Nikolai | |
| dc.creator | Grunewald, Fritz | |
| dc.creator | Kunyavskii, Boris | |
| dc.creator | Plotkin, Eugene | |
| dc.date | 2006-10-31 | |
| dc.date | 2007-12-25 | |
| dc.date.accessioned | 2026-07-07T08:52:13Z | |
| dc.date.available | 2026-07-07T08:52:13Z | |
| dc.description | We are looking for the smallest integer k>1 providing the following characterization of the solvable radical R(G) of any finite group G: R(G) coincides with the collection of all g such that for any k elements a_1,a_2,...,a_k the subgroup generated by the elements g, a_iga_i^{-1}, i=1,...,k, is solvable. We consider a similar problem of finding the smallest integer l>1 with the property that R(G) coincides with the collection of all g such that for any l elements b_1,b_2,...,b_l the subgroup generated by the commutators [g,b_i], i=1,...,l, is solvable. Conjecturally, k=l=3. We prove that both k and l are at most 7. In particular, this means that a finite group G is solvable if and only if in each conjugacy class of G every 8 elements generate a solvable subgroup. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610983 | |
| dc.identifier | http://arxiv.org/abs/math/0610983 | |
| dc.identifier | Groups, Geometry, and Dynamics 2 (2008), No. 1, 85-120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145208 | |
| dc.subject | Group Theory | |
| dc.title | A commutator description of the solvable radical of a finite group | |
| dc.type | text |