On certain questions of the free group automorphisms theory
| dc.creator | Bardakov, Valeriy G. | |
| dc.creator | Mikhailov, Roman | |
| dc.date | 2007-01-16 | |
| dc.date.accessioned | 2026-07-07T07:41:17Z | |
| dc.date.available | 2026-07-07T07:41:17Z | |
| dc.description | Certain subgroups of the groups $Aut(F_n)$ of automorphisms of a free group $F_n$ are considered. Comparing Alexander polynomials of two poly-free groups $Cb_4^+$ and $P_4$ we prove that these groups are not isomorphic, despite the fact that they have a lot of common properties. This answers the question of Cohen-Pakianathan-Vershinin-Wu from \cite{CVW}. The questions of linearity of subgroups of $Aut(F_n)$ are considered. As an application of the properties of poison groups in the sense of Formanek and Procesi, we show that the groups of the type $Aut(G*\mathbb Z)$ for certain groups $G$ and the subgroup of $IA$-automorphisms $IA(F_n)\subset Aut(F_n)$ are not linear for $n\geq 3$. This generalizes the recent result of Pettet that $IA(F_n)$ are not linear for $n\geq 5$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701441 | |
| dc.identifier | http://arxiv.org/abs/math/0701441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122053 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F36; 20F28; 20G15 | |
| dc.title | On certain questions of the free group automorphisms theory | |
| dc.type | text |