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arXiv · 1309.2897

The linearity problem for the unitriangular automorphism groups of free groups

V. Roman'kov
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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 $n \leq 3.$ 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.

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V. Roman'kov. 2013-09-11. The linearity problem for the unitriangular automorphism groups of free groups. https://arxiv.org/abs/1309.2897

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