Non-linear, solvable, residually $p$ groups

TL;DR

This paper constructs the first known examples of finitely generated non-linear solvable residually 2 groups, expanding the understanding of residually finite groups beyond linear cases.

Contribution

It provides explicit constructions of finitely generated non-linear solvable residually 2 groups, a previously unknown class of such groups.

Findings

First examples of finitely generated non-linear solvable residually 2 groups

Extends the landscape of residually finite groups beyond linear cases

Shows existence of non-linear solvable groups with residual properties

Abstract

In 2005, Borisov and Sapir proved that ascending HNN extensions of finitely generated linear groups are residually finite. Subsequently, Dru\c{t}u and Sapir noted the existence of finitely generated non-linear residually finite groups based on the work of Borisov and Sapir. In 2017, Kharlampovich, Myasnikov and Sapir showed that there exist finitely generated non-linear solvable residually finite groups. In this paper, we construct the first examples of finitely generated non-linear solvable residually 2 groups.