Non-linear, solvable, residually $p$ groups

Abstract

In 2005, Borisov and Sapir proved that ascending HNN extensions of finitely generated linear groups are residually finite. Subsequently, Druţu 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.

25 pages