The linearity problem for the unitriangular automorphism groups of free groups

arXiv1309.2897MaRDI QIDQ6244727

Vitaliĭ Roman'kov

Publication date: 11 September 2013

Abstract: We prove that the unitriangular automorphism group of a free group of rank $n$ has a faithful representation by matrices over a field, or in other words, it is a linear group, if and only if $nleq3.$ Thus, we have completed a description of relatively free groups with linear the unitriangular automorphism groups. This description was initiated by Erofeev and the author in cite{Erofeev}, where proper varieties of groups have been considered.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Automorphism groups of groups (20F28) Free nonabelian groups (20E05)

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