On certain questions of the free group automorphisms theory

Abstract

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 $C{b}_4^{+}$ 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 $Aut(G\ast \mathbb{Z})$ for certain groups $G$ and the subgroup of $IA$-automorphisms $IA(F_n)\subset Aut(F_n)$ are not linear for $n\ge 3$. This generalizes the recent result of Pettet that $IA(F_n)$ are not linear for $n\ge 5$.

11 pages

Cited by in corpus (1)

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