Geodesic
The linearity problem for the unitriangular automorphism groups of free groups
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 516-520

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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 $n\leq3$. 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 [1], where proper varieties of groups have been considered.
Keywords: free group, unitriangular automorphism, linearity. 
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     title = {The linearity problem for the unitriangular automorphism groups of free groups},
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Vitaly A. Roman'kov. The linearity problem for the unitriangular automorphism groups of free groups. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 516-520. http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a11/