English

The linearity problem for the unitriangular automorphism groups of free groups

Group Theory 2020-10-19 v1

Abstract

We prove that the unitriangular automorphism group of a free group of rank nn has a faithful representation by matrices over a field, or in other words, it is a linear group, if and only if n3.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.

Keywords

Cite

@article{arxiv.1309.2897,
  title  = {The linearity problem for the unitriangular automorphism groups of free groups},
  author = {V. Roman'kov},
  journal= {arXiv preprint arXiv:1309.2897},
  year   = {2020}
}
R2 v1 2026-06-22T01:25:04.536Z